Acosta, G. and Durán, R. G.. An optimal Poincaré inequality in L¹ for convex domains. Proc. Amer. Math. Soc., 132(1):195–202, 2004.Google Scholar

Aldous, D. J. Unconditional bases and martingales in L_p(F). Math. Proc. Cambridge Philos. Soc., 85(1):117–123, 1979.Google Scholar

Aleksandrov, A. B. Spectral subspaces of the space L^p, p < 1. Algebra i Analiz, 19(3):1–75, 2007.Google Scholar

Anisimov, D. S. and Kislyakov, S. V.. Double singular integrals: interpolation and correction. Algebra i Analiz, 16(5):1–33, 2004.Google Scholar

Arai, H. Measures of Carleson type on filtrated probability spaces and the corona theorem on complex Brownian spaces. Proc. Amer. Math. Soc., 96(4):643–647, 1986a.Google Scholar

Arai, H. On the algebra of bounded holomorphic martingales. Proc. Amer. Math. Soc., 97(4):616–620, 1986b.Google Scholar

Asmar, N. and Hewitt, E.. Marcel Riesz’s theorem on conjugate Fourier series and its descendants. In Proceedings of the Analysis Conference, Singapore 1986, volume 150 of North-Holland Math. Stud., pages 1–56. North-Holland, Amsterdam, 1988.Google Scholar

Bass, R. F. Probabilistic Techniques in Analysis. Probability and its Applications. Springer-Verlag, New York, 1995.Google Scholar

Beauzamy, B. Introduction to Banach Spaces and Their Geometry, volume 68 of North-Holland Math. Stud. North-Holland, Amsterdam-New York, 1982.Google Scholar

Bedrosian, E. A product theorem for Hilbert transforms. Proceedings of the IEEE, 51(5):868–869, May 1963.Google Scholar

Benedek, A., Calerón, A.-P., and Panzone, R.. Convolution operators on Banach space valued functions. Proc. Nat. Acad. Sci. USA, 48:356–365, 1962.Google Scholar

Bennett, C. and Sharpley, R.. Interpolation of Operators, volume 129 of Pure and Applied Mathematics. Academic Press, Inc., Boston, MA, 1988.Google Scholar

Benyamini, Y. and Lindenstrauss, J.. Geometric Nonlinear Functional Analysis. Vol. 1, American Mathematical Society Colloquium Publications, vol. 48. American Mathematical Society, Providence, RI, 2000.Google Scholar

Bessaga, C. and Pełczyński, A.. A generalization of results of R. C. James concerning absolute bases in Banach spaces. Studia Math., 17:165–174, 1958a.Google Scholar

Bessaga, C. and Pełczyński, A.. On bases and unconditional convergence of series in Banach spaces. Studia Math., 17:151–164, 1958b.CrossRefGoogle Scholar

Blasco, O. and Pełczyński, A.. Theorems of Hardy and Paley for vector-valued analytic functions and related classes of Banach spaces. Trans. Amer. Math. Soc., 323(1):335–367, 1991.Google Scholar

Blower, G. A multiplier characterization of analytic UMD spaces. Studia Math., 96(2):117–124, 1990.CrossRefGoogle Scholar

Blower, G. and Ransford, T.. Complex uniform convexity and Riesz measures. Canad. J. Math., 56(2):225–245, 2004.Google Scholar

Bochner, S. Additive set functions on groups. Ann. Math. (2), 40:769–799, 1939.Google Scholar

Bochner, S. Generalized conjugate and analytic functions without expansions. Proc. Nat. Acad. Sci. USA., 45:855–857, 1959.Google Scholar

Bogachev, V. I. Measure theory. Vol. I, II.Springer-Verlag, Berlin, 2007.CrossRefGoogle Scholar

Bonami, A. Étude des coefficients de Fourier des fonctions de L^p(G). Ann. Inst. Fourier (Grenoble), 20(2):335–402, 1970.Google Scholar

Bourgain, J. La Propriete de Radon–Nikodym. Publications Mathematiques de l’Universite Pierre et Marie Curie No. 36, Paris, 1979.Google Scholar

Bourgain, J. Complémentation de sous-espaces L¹ dans les espaces L¹. In Seminar on Functional Analysis, 1979–1980 (French), Exp. No. 27, 7. École Polytech., Palaiseau, 1980a.Google Scholar

Bourgain, J. Walsh subspaces of L^p-product spaces. In Seminar on Functional Analysis, 1979–1980 (French), Exp. No. 4A, 9. École Polytech., Palaiseau, 1980b.Google Scholar

Bourgain, J. A counterexample to a complementation problem. Compositio Math., 43(1):133–144, 1981.Google Scholar

Bourgain, J. Embedding L¹ in L¹/H¹. Trans. Amer. Math. Soc., 278(2):689–702, 1983a.Google Scholar

Bourgain, J. On the primarity of H^∞-spaces. Israel J. Math., 45(4):329–336, 1983b.CrossRefGoogle Scholar

Bourgain, J. Some remarks on Banach spaces in which martingale difference sequences are unconditional. Ark. Mat., 21(2):163–168, 1983c.Google Scholar

Bourgain, J. Bilinear forms on H^∞ and bounded bianalytic functions. Trans. Amer. Math. Soc., 286(1):313–337, 1984a.Google Scholar

Bourgain, J. The dimension conjecture for polydisc algebras. Israel J. Math., 48(4):289–304, 1984b.CrossRefGoogle Scholar

Bourgain, J. Martingale transforms and geometry of Banach spaces. In Israel Seminar on Geometrical Aspects of Functional Analysis (1983/84), pages XIV, 16. Tel Aviv University, Tel Aviv, 1984.Google Scholar

Bourgain, J. New Banach space properties of the disc algebra and H^∞. Acta Math., 152(1-2):1–48, 1984d.Google Scholar

Bourgain, J. On martingales transforms in finite-dimensional lattices with an appendix on the K-convexity constant. Math. Nachr., 119:41–53, 1984e.Google Scholar

Bourgain, J. Some results on the bidisc algebra. Astérisque, 131:279–298, 1985.Google Scholar

Bourgain, J. Homogeneous polynomials on the ball and polynomial bases. Israel J. Math., 68(3):327–347, 1989.Google Scholar

Bourgain, J. and Davis, W. J.. Martingale transforms and complex uniform convexity. Trans. Amer. Math. Soc., 294(2):501–515, 1986.Google Scholar

Bu, S. Q. Quelques remarques sur la propriété de Radon–Nikodým analytique. C. R. Acad. Sci. Paris Sér. I Math., 306(18):757–760, 1988.Google Scholar

Bu, S. Q. On the analytic Radon–Nikodým property for bounded subsets in Banach spaces. J. London Math. Soc. (2), 47(3):484–496, 1993.CrossRefGoogle Scholar

Bu, S. Q. and Khaoulani, B.. Une caractérisation de la propriété de Radon–Nikodým analytique pour les espaces de Banach isomorphes à leur carrés. Math. Ann., 288(2):345–360, 1990.Google Scholar

Bu, S. Q. and Schachermayer, W.. Approximation of Jensen measures by image measures under holomorphic functions and applications. Trans. Amer. Math. Soc., 331(2):585–608, 1992.Google Scholar

Buhvalov, A. V. Hardy spaces of vector-valued functions. Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 65:5–16, 203, 1976.Google Scholar

Bukhvalov, A. V. Hardy spaces of vector-valued functions. J. Sov. Math., 16:1051–1059, 1981.Google Scholar

Bukhvalov, A. V. and Danilevich, A. A.. Boundary properties of analytic and harmonic functions with values in a Banach space. Mat. Zametki, 31(2):203–214, 317, 1982.Google Scholar

Burkholder, D. L. Distribution function inequalities for martingales. Ann. Probability, 1:19–42, 1973.Google Scholar

Burkholder, D. L. A sharp inequality for martingale transforms. Ann. Probab., 7(5):858–863, 1979.Google Scholar

Burkholder, D. L. Martingale transforms and the geometry of Banach spaces. In Probability in Banach Spaces, III (Medford, Mass., 1980), volume 860 of Lecture Notes in Math., pages 35–50. Springer, Berlin-New York, 1981.Google Scholar

Burkholder, D. L. A geometric condition that implies the existence of certain singular integrals of Banach-space-valued functions. In Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981), Wadsworth Math. Ser., pages 270–286. Wadsworth, Belmont, CA, 1983.Google Scholar

Burkholder, D. L. Differential subordination of harmonic functions and martingales. In Harmonic Analysis and Partial Differential Equations (El Escorial, 1987), volume 1384 of Lecture Notes in Math., pages 1–23. Springer, Berlin, 1989.Google Scholar

Burkholder, D. L. Martingales and singular integrals in Banach spaces. In Handbook of the Geometry of Banach Spaces, Vol. I, pages 233–269. North-Holland, Amsterdam, 2001.Google Scholar

Burkholder, D. L., Davis, B. J., and Gundy, R. F.. Integral inequalities for convex functions of operators on martingales. In Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability (Univ. California, Berkeley, Calif., 1970/1971), Vol. II: Probability Theory, pages 223–240, 1972.Google Scholar

Burkholder, D. L. and Gundy, R. F.. Extrapolation and interpolation of quasi-linear operators on martingales. Acta Math., 124:249–304, 1970.Google Scholar

Burkholder, D. L., Gundy, R. F., and Silverstein, M. L.. A maximal function characterization of the class H^p. Trans. Amer. Math. Soc., 157:137–153, 1971.Google Scholar

Calderón, A.-P. Intermediate spaces and interpolation, the complex method. Studia Math., 24:113–190, 1964.Google Scholar

Capon, M. Primarité de l_p(L¹). Math. Ann., 250(1):55–63, 1980.Google Scholar

Carleson, L. On convergence and growth of partial sums of Fourier series. Acta Math., 116:135–157, 1966.Google Scholar

Carne, K. The algebra of bounded holomorphic martingales. J. Funct. Anal., 45(1):95–108, 1982.Google Scholar

Chang, S.-Y. A., Wilson, J. M., and Wolff, T. H.. Some weighted norm inequalities concerning the Schrödinger operators. Comment. Math. Helv., 60(2):217–246, 1985.CrossRefGoogle Scholar

Chatterji, S. D. Martingale convergence and the Radon–Nikodym theorem in Banach spaces. Math. Scand., 22:21–41, 1968.Google Scholar

Coifman, R. R., Jones, P. W., and Semmes, S.. Two elementary proofs of the L2 boundedness of Cauchy integrals on Lipschitz curves. J. Amer. Math. Soc., 2(3):553–564, 1989.Google Scholar

David, G. Wavelets and Singular Integrals on Curves and Surfaces, volume 1465 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1991.Google Scholar

David, G. Unrectifiable 1-sets have vanishing analytic capacity. Rev. Mat. Iberoameri- cana, 14(2):369–479, 1998.CrossRefGoogle Scholar

Davis, B. On the integrability of the martingale square function. Israel J. Math., 8:187–190, 1970.Google Scholar

Davis, W. J., Figiel, T., Johnson, W. B., and Pelczynski, A.. Factoring weakly compact operators. J. Funct. Anal., 17:311–327, 1974.Google Scholar

Davis, W. J., Garling, D. J. H., and Tomczak-Jaegermann, N.. The complex convexity of quasinormed linear spaces. J. Funct. Anal., 55(1):110–150, 1984.Google Scholar

Davis, W. J., Ghoussoub, N., Johnson, W. B., Kwapień, S., and Maurey, B.. Weak convergence of vector valued martingales. In Probability in Banach Spaces 6 (Sandbjerg, 1986), volume 20 of Progr. Probab., pages 41–50. Birkhäuser Boston, Boston, MA, 1990.Google Scholar

Dechamps-Gondim, M. Analyse harmonique, analyse complexe et géométrie des espaces de Banach (d’après Jean Bourgain). Astérisque, 1983(121–122):171–195, 1985. Seminar Bourbaki, Vol. 1983/84.Google Scholar

Delbaen, F. and Schachermayer, W.. An inequality for the predictable projection of an adapted process. In Séminaire de Probabilités, XXIX, volume 1613 of Lecture Notes in Math., pages 17–24. Springer, Berlin, 1995.Google Scholar

Dellacherie, C. and Meyer, P.-A.. Probabilités et potentiel. Hermann, Paris, 1975. Chapitres I à IV, Édition entièrement refondue, Publications de l’Institut de Mathématique de l’Université de Strasbourg, No. XV, Actualités Scientifiques et Industrielles, No. 1372.Google Scholar

Dellacherie, C. and Meyer, P.-A.. Probabilities and Potential, volume 29 of North-Holland Math. Stud. North-Holland, Amsterdam-New York, 1978.Google Scholar

Dellacherie, C. and Meyer, P.-A.. Probabilities and Potential B Theory of Martingales, volume 72 of North-Holland Math. Stud. North-Holland, Amsterdam, 1982.Google Scholar

Diestel, J. Geometry of Banach Spaces – Selected Topics. Lecture Notes in Mathematics, Vol. 485. Springer-Verlag, Berlin-New York, 1975.Google Scholar

Diestel, J., Jarchow, H., and Tonge, A.. Absolutely Summing Operators, volume 43 of Camb. Stud. Adv. Math. Cambridge University Press, Cambridge, 1995.Google Scholar

Diestel, J. and Uhl, J. J. Jr.. Vector Measures. American Mathematical Society, Providence, R.I., 1977.Google Scholar

Dieudonné, J. Éléments d’analyse. Tome I: Fondements de l’analyse moderne. Traduit de l’anglais par D. Huet. Avant-propos de G. Julia. Nouvelle édition revue et corrigée. Cahiers Scientifiques, Fasc. XXVIII. Gauthier-Villars, Éditeur, Paris, 1968a.Google Scholar

Dieudonné, J. Éléments d’analyse. Tome II: Chapitres XII à XV. Cahiers Scientifiques, Fasc. XXXI. Gauthier-Villars, Éditeur, Paris, 1968b.Google Scholar

Dilworth, S. J. Complex convexity and the geometry of Banach spaces. Math. Proc. Camb. Philos. Soc., 99(3):495–506, 1986.Google Scholar

Doob, J. L. Stochastic Processes. Wiley, New York, 1953.Google Scholar

Doob, J. L. Semimartingales and subharmonic functions. Trans. Amer. Math. Soc., 77:86–121, 1954.Google Scholar

Dor, L. E. On projections in L¹. Ann. Math. (2), 102(3):463–474, 1975.Google Scholar

Dosev, D., Johnson, W. B., and Schechtman, G.. Commutators on L_p, 1 ≤ p < ∞. J. Am. Math. Soc., 26(1):101–127, 2013.Google Scholar

Dowling, P. N. Representable operators and the analytic Radon–Nikodým property in Banach spaces. Proc. R. Ir. Acad. Sect. A, 85(2):143–150, 1985.Google Scholar

Dowling, P. N. and Edgar, G. A.. Some characterizations of the analytic Radon– Nikodým property in Banach spaces. J. Funct. Anal., 80(2):349–357, 1988.Google Scholar

Dunford, N. and Pettis, B. J.. Linear operations on summable functions. Trans. Am. Math. Soc., 47:323–392, 1940.CrossRefGoogle Scholar

Durrett, R. Brownian Motion and Martingales in Analysis. Wadsworth Mathematics Series. Wadsworth International Group, Belmont, CA, 1984.Google Scholar

Edgar, G. A. Disintegration of measures and the vector-valued Radon–Nikodým theorem. Duke Math. J., 42(3):447–450, 1975.Google Scholar

Edgar, G. A. Complex martingale convergence. In Kalton, N.J., Saab, E. (eds) Banach Spaces. Lecture Notes in Mathematics, vol 1166. Springer, Berlin, Heidelberg, 1985.Google Scholar

Edgar, G. A. Analytic martingale convergence. J. Funct. Anal., 69(2):268–280, 1986.Google Scholar

Enflo, P. and Starbird, T. W.. Subspaces of L¹ containing L¹. Studia Math., 65(2):203–225, 1979.Google Scholar

Fakhoury, H. Représentations d’opérateurs à valeurs dans L¹(X, Σ, μ). Math. Ann., 240(3):203–212, 1979.Google Scholar

Fetter, H. and Gamboa de Buen, B.. The James Forest, volume 236 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, 1997.Google Scholar

Föllmer, H. Stochastic holomorphy. Math. Ann., 207:245–255, 1974.Google Scholar

García-Cuerva, J. and Rubio de Francia, J. L.. Weighted Norm Inequalities and Related Topics, volume 116 of North-Holland Math. Stud. North-Holland, Amsterdam, 1985.Google Scholar

Garling, D. J. H. Brownian motion and UMD-spaces. In Probability and Banach Spaces (Zaragoza, 1985), volume 1221 of Lecture Notes in Math., pages 36–49. Springer, Berlin, 1986.Google Scholar

Garling, D. J. H On martingales with values in a complex Banach space. Math. Proc. Camb. Philos. Soc., 104(2):399–406, 1988.Google Scholar

Garling, D. J. H. Random martingale transform inequalities. In Probability in Banach Spaces 6 (Sandbjerg, 1986), volume 20 of Progr. Probab., pages 101–119. Birkhäuser Boston, Boston, MA, 1990.Google Scholar

Garling, D. J. H. Hardy martingales and the unconditional convergence of martingales. Bull. London Math. Soc., 23(2):190–192, 1991.Google Scholar

Garling, D. J. H. Inequalities: A Journey Into Linear Analysis. Cambridge University Press, Cambridge, 2007.Google Scholar

Garling, D. J. H. and Montgomery-Smith, S. J.. Complemented subspaces of spaces obtained by interpolation. J. London Math. Soc. (2), 44(3):503–513, 1991.Google Scholar

Garnett, J. B. Bounded Analytic Functions, volume 96 of Pure and Applied Mathematics. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1981.Google Scholar

Garnett, J. B. and Jones, P. W.. The distance in BMO to L^∞. Ann. of Math., 108(2):373–393, 1978.Google Scholar

Garnett, J. B. and Jones, P. W.. BMO from dyadic BMO. Pacific J. Math., 99(2):351–371, 1982.Google Scholar

Garsia, A. M. Martingale Inequalities: Seminar Notes on Recent Progress. W. A. Benjamin, Inc., Reading, Mass.-London-Amsterdam, 1973. Mathematics Lecture Notes Series.Google Scholar

Getoor, R. K. and Sharpe, M. J.. Conformal martingales. Invent. Math., 16:271–308, 1972.Google Scholar

Ghoussoub, N. Duality and Perturbation Methods in Critical Point Theory, volume 107 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1993.Google Scholar

Ghoussoub, N., Lindenstrauss, J., and Maurey, B.. Analytic martingales and plurisub-harmonic barriers in complex Banach spaces. In Banach Space Theory (Iowa City, IA, 1987), volume 85 of Contemp. Math., pages 111–130. Amer. Math. Soc., Providence, RI, 1989.Google Scholar

Ghoussoub, N. and Maurey, B.. H_δ-embedding in Hilbert space and optimization on G_δ-sets. Mem. Amer. Math. Soc., 62(349):101, 1986.Google Scholar

Ghoussoub, N. and Maurey, B.. Plurisubharmonic martingales and barriers in complex quasi-Banach spaces. Ann. Inst. Fourier (Grenoble), 39(4):1007–1060, 1989.Google Scholar

Ghoussoub, N., Maurey, B., and Schachermayer, W.. Pluriharmonically dentable complex Banach spaces. J. Reine Angew. Math., 402:76–127, 1989.Google Scholar

Ghoussoub, N. and Rosenthal, H. P.. Martingales, G_δ-embeddings and quotients of L¹. Math. Ann., 264(3):321–332, 1983.Google Scholar

Godefroy, G., Kalton, N. J., and Li, D.. Operators between subspaces and quotients of L¹. Indiana Univ. Math. J., 49(1):245–286, 2000.Google Scholar

Gohberg, I. C. and Krein, M. G.. Theory and Applications of Volterra Operators in Hilbert Space. Translated from the Russian by Feinstein, A.. Translations of Mathematical Monographs, Vol. 24. American Mathematical Society, Providence, R.I., 1970.Google Scholar

Grossetête, C. Sur certaines classes de fonctions harmoniques dans le disque à valeur dans un espace vectoriel topologique localement convexe. C. R. Acad. Sci. Paris Sér. A-B, 273:A1048–A1051, 1971.Google Scholar

Grossetête, C. Classes de Hardy et de Nevanlinna pour les fonctions holomorphes à valeurs vectorielles. C. R. Acad. Sci. Paris Sér. A-B, 274:A251–A253, 1972.Google Scholar

Haagerup, U. and Pisier, G.. Factorization of analytic functions with values in noncommutative L₁-spaces and applications. Canad. J. Math., 41(5):882–906, 1989.Google Scholar

Heins, M. Hardy Classes on Riemann Surfaces. Lecture Notes in Mathematics, No. 98. Springer-Verlag, Berlin-New York, 1969.Google Scholar

Helson, H. Conjugate series and a theorem of Paley. Pacific J. Math., 8:437–446, 1958.Google Scholar

Helson, H. Conjugate series in several variables. Pacific J. Math., 9:513–523, 1959.Google Scholar

Henkin, G. M. The nonisomorphy of certain spaces of functions of different numbers of variables. Funkcional. Anal. i Priložen., 1(4):57–68, 1967.Google Scholar

Henkin, G. M. The Banach spaces of analytic functions in a ball and in a bicylinder are nonisomorphic. Funkcional. Anal. i Priložen., 2(4):82–91, 1968.Google Scholar

Henkin, G. M. On non-isomorphism of Banach spaces of holomorphic functions. Studia Math., 38:267–270, 1970.Google Scholar

Hensgen, W. Hardy–Räume vektorwertiger Funktionen. Dissertation Ludwig-Maximilians-Universität München, pages 1–151, 1986.Google Scholar

Hensgen, W. Operatoren H¹ → X. Manuscripta Math., 59(4):399–422, 1987.Google Scholar

Hensgen, W. Some remarks on boundary values of vector-valued harmonic and analytic functions. Arch. Math. (Basel), 57(1):88–96, 1991.Google Scholar

Hoffmann-Jorgensen, J. Sums of independent Banach space valued random variables. Studia Math., 52:159–186, 1974.Google Scholar

Hunt, R., Muckenhoupt, B., and Wheeden, R.. Weighted norm inequalities for the conjugate function and Hilbert transform. Trans. Amer. Math. Soc., 176:227–251, 1973.Google Scholar

Hunt, R. A. On the convergence of Fourier series. In Orthogonal Expansions and their Continuous Analogues (Proc. Conf., Edwardsville, Ill., 1967), pages 235–255. Southern Illinois Univ. Press, Carbondale, Ill., 1968.Google Scholar

Hytönen, T., van Neerven, J., Veraar, M., and Weis, L.. Analysis in Banach Spaces. Vol. I. Martingales and Littlewood-Paley Theory Springer, Cham, 2016.Google Scholar

Itô, K., and McKean, H. P. Jr. Diffusion processes and their sample paths. Springer-Verlag, Berlin-New York, 1965.Google Scholar

Ivanisvili, P., Lindenberger, A., Müller, P. F. X., and Schmuckenschläger, M.. Hyper contractivity on the unit circle for ultraspherical measures: linear case. arXiv:2004.05567, DOI: 10.4171/RMI/1305, 2020.Google Scholar

James, R. C. Bases and reflexivity of Banach spaces. Ann. of Math., 52:518–527, 1950.Google Scholar

James, R. C. A separable somewhat reflexive Banach space with nonseparable dual. Bull. Am. Math. Soc., 80:738–743, 1974.Google Scholar

Jiao, Y., Randrianantoanina, N., Wu, L., and Zhou, D.. Square functions for noncommutative differentially subordinate martingales. Comm. Math. Phys., 374(2):975–1019, 2020.Google Scholar

Jiao, Y., Xie, G., and Zhou, D.. Dual spaces and John–Nirenberg inequalities of martingale Hardy–Lorentz–Karamata spaces. Q. J. Math., 66(2):605–623, 2015.Google Scholar

Jiao, Y., Wu, L., Yang, A., and Yi, R.. The predual and John–Nirenberg inequalities on generalized BMO martingale spaces. Trans. Am. Math. Soc., 369(1):537–553, 2017.Google Scholar

Johnson, W. B., Maurey, B., and Schechtman, G.. Weakly null sequences in L₁. J. Am. Math. Soc., 20(1):25–36, 2007.Google Scholar

Jones, P. W. L^∞ estimates for the problem in a half-plane. Acta Math., 150(1–2):137–152, 1983.Google Scholar

Jones, P. W. and Müller, P. F. X.. Conditioned Brownian motion and multipliers into SL^∞. Geom. Funct. Anal., 14(2):319–379, 2004.Google Scholar

Kadec, M. I. and Pełczyński, A.. Bases, lacunary sequences and complemented subspaces in the spaces L ⊂ p. Studia Math., 21:161–176, 1961/62.Google Scholar

Kahane, J.-P. Some Random Series of Functions. D. C. Heath and Co. Raytheon Education Co., Lexington, Mass., 1968.Google Scholar

Kahane, J.-P. Some Random Series of Functions, volume 5 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, second edition, 1985.Google Scholar

Kalton, N. J. The endomorphisms of L_p(0 ≤ p ≤ i). Indiana Univ. Math. J., 27(3):353–381, 1978.Google Scholar

Kalton, N. J. Embedding L₁ in a Banach lattice. Israel J. Math., 32(2-3):209–220, 1979.Google Scholar

Kalton, N. J. Linear operators on L_p for 0 < p < 1. Trans. Am. Math. Soc., 259(2): 319–355, 1980.Google Scholar

Kalton, N. J. Banach spaces embedding into L₀. Israel J. Math., 52(4):305–319, 1985.Google Scholar

Kalton, N. J. Differentiability properties of vector valued functions. In Probability and Banach Spaces (Zaragoza, 1985), volume 1221 of Lecture Notes in Math., pages 141–181. Springer, Berlin, 1986a.Google Scholar

Kalton, N. J. Some applications of vector-valued analytic and harmonic functions. In Probability and Banach spaces (Zaragoza, 1985), volume 1221 of Lecture Notes in Math., pages 114–140. Springer, Berlin, 1986b.Google Scholar

Kalton, N. J. and Pełczyński, A.. Kernels of surjections from L₁-spaces with an application to Sidon sets. Math. Ann., 309(1):135–158, 1997.Google Scholar

Kalton, N. J. and Weis, L.. The H^∞-calculus and sums of closed operators. Math. Ann., 321(2):319–345, 2001.Google Scholar

Katznelson, Y. An Introduction to Harmonic Analysis. John Wiley & Sons, Inc., New York-London-Sydney, 1968.Google Scholar

Kazaniecki, K. and Wojciechowski, M.. On the equivalence between the sets of the trigonometric polynomials. arXiv:1502.05994, 2014.Google Scholar

Kislyakov, S. V. What is needed for a 0-absolutely summing operator to be nuclear? In Complex Analysis and Spectral Theory (Leningrad, 1979/1980), volume 864 of Lecture Notes in Math., pages 336–364. Springer, Berlin-New York, 1981.Google Scholar

Kislyakov, S. V. Spaces with a “small” annihilator. Zap. Naučn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI), 65:192–195, 209, 1976.Google Scholar

Kislyakov, S. V. Absolutely summing operators on the disc algebra. Algebra i Analiz, 3(4):1–77, 1991.Google Scholar

König, H. On the best constants in the Khintchine inequality for Steinhaus variables. Israel J. Math., 203(1):23–57, 2014.Google Scholar

Koosis, P. Introduction to Hp Spaces, volume 40 of London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge-New York, 1980.Google Scholar

Kuratowski, K. and Ryll-Nardzewski, C.. A general theorem on selectors. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 13:397–403, 1965.Google Scholar

Kwapień, S. Unsolved problems (problem 3). Studia Math., 38:467–483, 1970.Google Scholar

Kwapień, S. On the form of a linear operator in the space of all measurable functions. Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys., 21:951–954, 1973.Google Scholar

Kwapień, S. On Banach spaces containing c₀. Studia Math., 52:187–188, 1974. A supplement to the paper by J. Hoffmann-Jorgensen “Sums of independent Banach space valued random variables” (Studia Math. 52 (1974), 159–186).Google Scholar

Kwapień, S. and Pełczyński, A.. The main triangle projection in matrix spaces and its applications. Studia Math., 34:43–68, 1970.CrossRefGoogle Scholar

Kwapien, S. and Woyczyński, W. A.. Random Series and Stochastic Integrals: Single and Multiple. Probability and its Applications. Birkhäuser Boston Inc., Boston, MA, 1992.Google Scholar

Lechner, R. Factorization in SL^∞. Israel J. Math., 226(2):957–991, 2018.Google Scholar

Lechner, R. Dimension dependence of factorization problems: Hardy spaces and . Israel J. Math., 232(2):677–693, 2019.Google Scholar

Lechner, R., Motakis, P., Müller, P. F. X., and Schlumprecht, T.. The factorisation property of l^∞(X_k). Math. Proc. Camb. Philos. Soc., 171(2):421–448, 2021Google Scholar

Lechner, R., Motakis, P., Müller, P. F. X., and Schlumprecht, T.. Strategically reproducible bases and the factorization property. Israel J. Math., 238(1):13–60, 2020.Google Scholar

Lépingle, D. Une inégalité de martingales. In Séminaire de Probabilités, XII (Univ. Strasbourg, Strasbourg, 1976/1977), volume 649 of Lecture Notes in Math., pages 134–137. Springer, Berlin, 1978.Google Scholar

Lévy, P. Processus stochastiques et mouvement Brownien. Suivi d’une note de M. Loève. Gauthier-Villars, Paris, 1948.Google Scholar

Lewis, D. R. and Stegall, C.. Banach spaces whose duals are isomorphic to l₁(Γ). J. Funct. Anal., 12:177–187, 1973.Google Scholar

Li, D. and Queffélec, H.. Introduction à l’étude des espaces de Banach, volume 12 of Cours Spécialisés. Société Mathématique de France, Paris, 2004.Google Scholar

Li, D. and Queffélec, H.. Introduction to Banach Spaces: Analysis and Probability. Vol. 1, volume 166 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2018. Translated from the French by Danièle Gibbons and Greg Gibbons, For the French original see [MR2124356].Google Scholar

Lindenstrauss, J. and Pełczyński, A.. Contributions to the theory of the classical Banach spaces. J. Funct. Anal., 8:225–249, 1971.Google Scholar

Lindenstrauss, J. and Rosenthal, H. P.. The spaces. Israel J. Math., 7:325–349, 1969.Google Scholar

Lindenstrauss, J. and Stegall, C.. Examples of separable spaces which do not contain ℓ₁ and whose duals are non-separable. Studia Math., 54(1):81–105, 1975.Google Scholar

Lindenstrauss, J. and Tzafriri, L.. Classical Banach Spaces. I. Springer-Verlag, Berlin-New York, 1977.Google Scholar

Littlewood, J. E. Mathematical Notes (8); On Functions Subharmonic in a Circle (II). Proc. London Math. Soc. (2), 28(5):383–394, 1928.Google Scholar

Liu, Z. A decomposition theorem for operators on L¹. J. Operator Theory, 40(1):3–34, 1998.Google Scholar

Long, R. L. Martingale Spaces and Inequalities. Peking University Press, Beijing; Friedr. Vieweg & Sohn, Braunschweig, 1993.Google Scholar

Marcus, M. B. and Pisier, G.. Random Fourier Series with Applications to Harmonic Analysis, Ann. Math. Stud., 101:1–150, 1981.Google Scholar

Maslyuchenko, O. V., Mykhaylyuk, V. V., and Popov, M. M.. A lattice approach to narrow operators. Positivity, 13(3):459–495, 2009.Google Scholar

Maurey, B. Théorèmes de factorisation pour les opérateurs linéaires àvaleurs dans un espace L^p(U, μ), 0 < p ≤ +∞. In Séminaire Maurey–Schwartz Année 1972–1973: Espaces L^p et applications radonifiantes, Exp. No. 15, page 8. Centre de Math., École Polytech., Paris, 1973a.Google Scholar

Maurey, B. Un lemme de H. P. Rosenthal. In Séminaire Maurey-Schwartz Année 1972–1973: Espaces L^p et applications radonifiantes, Exp. No. 21, page 11. Centre de Math., École Polytech., Paris, 1973b.Google Scholar

Maurey, B. Théorèmes de factorisation pour les opérateurs linéaires à valeurs dans les espaces L^p. Société Mathématique de France, Paris, 1974.Google Scholar

Maurey, B. Sous-espaces complémentés de L^p, d’après P. Enflo. In Séminaire Maurey-Schwartz 1974–1975: Espaces L^p, applications radonifiantes et géométrie des espaces de Banach, Exp. No. III, pages 15 pp. (erratum, p. 1). 1975a.Google Scholar

Maurey, B. Système de Haar. In Séminaire Maurey-Schwartz 1974–1975: Espaces L^p, applications radonifiantes et géométrie des espaces de Banach, Exp. Nos. I et II, pages 26 pp. (erratum, p. 1). Centre Math., École Polytech., Paris, 1975b.Google Scholar

Maurey, B. Isomorphismes entre espaces H¹. Acta Math., 145(1–2):79–120, 1980.Google Scholar

Maurey, B. and Pisier, G.. Séries de variables aléatoires vectorielles indépendantes et propriétés géométriques des espaces de Banach. Studia Math., 58(1):45–90, 1976.Google Scholar

Maurey, B. and Rosenthal, H. P.. Normalized weakly null sequence with no unconditional subsequence. Studia Math., 61(1):77–98, 1977.Google Scholar

Maurey, B. and Schechtman, G.. Some remarks on symmetric basic sequences in L¹. Compos. Math., 38(1):67–76, 1979.Google Scholar

Meyer, P. A. Démonstration probabiliste de certaines inégalités de Littlewood–Paley. IV. Semi-groupes de convolution symétriques. In Séminaire de Probabilités, X (Première partie, Univ. Strasbourg, Strasbourg, année universitaire 1974/1975), pages 175–183. Lecture Notes in Math., Vol. 511. 1976.Google Scholar

Meyer, Y. Endomorphismes des ideaux fermes de L¹ (G), classes de Hardy et series de Fourier lacunaires. Ann. Sci. École Norm. Sup. (4), 1:499–580, 1968.Google Scholar

Mitiagin, B. S. and Pełczyński, A.. On the non-existence of linear isomorphisms between Banach spaces of analytic functions of one and several complex variables. Studia Math., 56(2):175–186, 1976.Google Scholar

Montgomery-Smith, S. Concrete representation of martingales. Electron. J. Probab., 3:No. 15, 15 pp. 1998.Google Scholar

Müller, P. F. X. Holomorphic martingales and interpolation between Hardy spaces. J. Anal. Math., 61:327–337, 1993.Google Scholar

Müller, P. F. X. Isomorphisms Between H¹ spaces, volume 66 of Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series) Birkhäuser Verlag, Basel, 2005.Google Scholar

Müller, P. F. X. A decomposition for Hardy martingales. Indiana Univ. Math. J., 61(5):1801–1816, 2012.Google Scholar

Müller, P. F. X. A decomposition for Hardy martingales II. Math. Proc. Camb. Philos. Soc., 157(2):189–207, 2014.Google Scholar

Müller, P. F. X. A decomposition for Hardy martingales III. Math. Proc. Camb. Philos. Soc., 162(1):173–189, 2017.Google Scholar

Müller, P. F. X. and Passenbrunner, M.. Almost everywhere convergence of spline sequences. Israel J. Math., 240(1):149–177, 2020.Google Scholar

Müller, P. F. X. and Penteker, J.. Lecture notes on singular integrals, projections, multipliers and rearrangements. In IMPAN Lecture Notes, Winter School on Harmonic Analysis, Bedlewo, www.impan.pl/swiat-matematyki/notatki-z-wyklado~/scriptsios_2.pdf, 2015.Google Scholar

Müller, P. F. X. and Riegler, K.. Radial variation of Bloch functions on the unit ball of Rd. Ark. Mat., 58(1):161–178, 2020.Google Scholar

Müller, P. F. X. and Yuditskii, P.. Interpolation for Hardy spaces: Marcinkiewicz decomposition, complex interpolation and holomorphic martingales. Colloq. Math., 158(1):141–155, 2019.Google Scholar

Neveu, J. Discrete-Parameter Martingales. North-Holland, Amsterdam-Oxford; American Elsevier Publishing Co., Inc., New York, revised edition, 1975. Translated from the French by Speed, T. P., North-Holland Mathematical Library, Vol. 10.Google Scholar

Novikov, I. and Semenov, E.. Haar Series and Linear Operators, volume 367 of Mathematics and its Applications. Kluwer Academic Publishers Group, Dordrecht, 1997.Google Scholar

Odell, E. and Zheng, B.. On the unconditional subsequence property. J. Funct. Anal., 258(2):604–615, 2010.Google Scholar

Osekowski, A. Sharp Martingale and Semimartingale Inequalities, volume 72 of Instytut Matematyczny Polskiej Akademii Nauk. Monografie Matematyczne (New Series). Birkhäuser/Springer Basel AG, Basel, 2012.Google Scholar

Pallares, A. and Kouba, O.. Seminar Notes. Groupe de Travail sur les Espaces de Banach. Equipe d’Analyse, Universite Paris VI, 1986-1987.Google Scholar

Parcet, J. and Randrianantoanina, N.. Gund’s decomposition for non-commutative martingales and applications. Proc. London Math. Soc. (3), 93(1):227–252, 2006.Google Scholar

Passenbrunner, M. Martingale inequalities for spline sequences. Positivity, 24(1):95–115, 2020.Google Scholar

Passenbrunner, M. Spline characterizations of the Radon–Nikodým property. Proc. Am. Math. Soc., 148(2):811–824, 2020.Google Scholar

Pełczyński, A. On the impossibility of embedding of the space L in certain Banach spaces. Colloq. Math., 8:199–203, 1961.Google Scholar

Pełczyński, A. Banach Spaces of Analytic Functions and Absolutely Summing Operators. American Mathematical Society, Providence, R.I., 1977. Expository lectures from the CBMS Regional Conference held at Kent State University, Kent, Ohio, July 11–16, 1976, Conference Board of the Mathematical Sciences Regional Conference Series in Mathematics, No. 30.Google Scholar

Pełczyński, A. Geometry of finite-dimensional Banach spaces and operator ideals. In Notes in Banach Spaces, pages 81–181. Univ. Texas Press, Austin, TX, 1980.Google Scholar

Pełczyński, A. and Wojciechowski, M.. Absolutely summing surjections from Sobolev spaces in the uniform norm. In Progress in Functional Analysis (Peñíscola, 1990), volume 170 of North-Holland Math. Stud., pages 423–431. North-Holland, Amsterdam, 1992a.Google Scholar

Pełczyński, A. and Wojciechowski, M.. Paley projections on anisotropic Sobolev spaces on tori. Proc. London Math. Soc. (3), 65(2):405–422, 1992b.Google Scholar

Penteker, J. Postorder rearrangement operators. Q. J. Math., 66(4):1103–1126, 2015.CrossRefGoogle Scholar

Perrin, M. A noncommutative Davis’ decomposition for martingales. J. Lond. Math. Soc. (2), 80(3):627–648, 2009.Google Scholar

Petersen, K. E. Brownian Motion, Hardy Spaces and Bounded Mean Oscillation. Cambridge University Press, Cambridge-New York-Melbourne, 1977. London Mathematical Society Lecture Note Series, No. 28.Google Scholar

Phelps, R. R. Convex Functions, Monotone Operators and Differentiability, volume 1364 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1989.Google Scholar

Pisier, G. Sur les espaces qui ne contiennent pas de uniformément. In Séminaire Maurey-Schwartz (1973–1974), Espaces L^p, applications radonifiantes et géométrie des espaces de Banach, Exp. No. 7, pages 19 pp. (errata, p. E.1). 1974.Google Scholar

Pisier, G. Martingales with values in uniformly convex spaces. Israel J. Math., 20(3–4):326–350, 1975a.Google Scholar

Pisier, G. Un exemple concernant la super-réflexivité. In Séminaire Maurey-Schwartz 1974–1975: Espaces L^p applications radonifiantes et géométrie des espaces de Banach, Annexe No. 2, page 12. 1975b.Google Scholar

Pisier, G. Une nouvelle classe d’espaces de Banach vérifiant le théorème de Grothendieck. Ann. Inst. Fourier, 28(1):x, 69–90, 1978.Google Scholar

Pisier, G. Some applications of the complex interpolation method to Banach lattices. J. Anal. Math., 35:264–281, 1979.Google Scholar

Pisier, G. Sur les espaces de Banach K-convexes. In Seminar on Functional Analysis, 1979–1980 (French), pages Exp. No. 11, 15. École Polytech., Palaiseau, 1980.Google Scholar

Pisier, G. Holomorphic semigroups and the geometry of Banach spaces. Ann. Math. (2), 115(2):375–392, 1982a.Google Scholar

Pisier, G. Quotients of Banach spaces of cotype q. Proc. Am. Math. Soc., 85(1):32–36, 1982b.Google Scholar

Pisier, G. Counterexamples to a conjecture of Grothendieck. Acta Math., 151(3–4):181–208, 1983.Google Scholar

Pisier, G. Factorization of Linear Operators and Geometry of Banach Spaces, volume 60 of CBMS Regional Conference Series in Mathematics. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986.Google Scholar

Pisier, G. Factorization of operator valued analytic functions. Adv. Math., 93(1):61–125, 1992a.Google Scholar

Pisier, G. Interpolation between H^p spaces and noncommutative generalizations. I. Pacific J. Math., 155(2):341–368, 1992b.Google Scholar

Pisier, G. Interpolation between H^p spaces and noncommutative generalizations. II. Rev. Mat. Iberoamericana, 9(2):281–291, 1993.Google Scholar

Pisier, G. A polynomially bounded operator on Hilbert space which is not similar to a contraction. arXiv: arxiv.org/abs/math/9602207, 1996.Google Scholar

Pisier, G. A polynomially bounded operator on Hilbert space which is not similar to a contraction. J. Am. Math. Soc., 10(2):351–369, 1997.Google Scholar

Pisier, G. Martingales in Banach Spaces, volume 155 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 2016.Google Scholar

Pisier, G. and Xu, Q.. Non-commutative martingale inequalities. Comm. Math. Phys., 189(3):667–698, 1997.Google Scholar

Popov, M. and Randrianantoanina, B.. Narrow Operators on Function Spaces and Vector Lattices, volume 45 of De Gruyter Studies in Mathematics. Walter de Gruyter & Co., Berlin, 2013.Google Scholar

Qiu, Y. On the UMD constants for a class of iterated L_p(L_q) spaces. J. Funct. Anal., 263(8):2409–2429, 2012a.Google Scholar

Qiu, Y. Propriété UMD pour les espaces de Banach et d’opérateurs. Thèse de Doctorat, Université Pierre et Marie Curie, 2012b.Google Scholar

Randrianantoanina, N. Conditioned square functions for noncommutative martingales. Ann. Probab., 35(3):1039–1070, 2007.Google Scholar

Randrianantoanina, N. Wu, L. and Xu, Q. Noncommutative Davis type decompositions and applications. J. Lond. Math. Soc. (2), 99(1):97–126, 2019.Google Scholar

Ransford, T. Potential Theory in the Complex Plane, volume 28 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 1995.Google Scholar

Revuz, D. and Yor, M.. Continuous Martingales and Brownian Motion, volume 293 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences]. Springer-Verlag, Berlin, 1991.Google Scholar

Rosenthal, H. P. On subspaces of L^p. Ann. Math. (2), 97:344–373, 1973.Google Scholar

Rosenthal, H. P. Sign-embeddings of L¹. In Banach Spaces, Harmonic Analysis, and Probability Theory (Storrs, Conn., 1980/1981), volume 995 of Lecture Notes in Math., pages 155–165. Springer, Berlin, 1983.Google Scholar

Rosenthal, H. P. Embeddings of L¹ in L¹. In Conference in Modern Analysis and Probability (New Haven, Conn., 1982), volume 26 of Contemp. Math., pages 335–349. Amer. Math. Soc., Providence, RI, 1984.Google Scholar

Rudin, W. Real and Complex Analysis. McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, second edition, 1974.Google Scholar

Rudin, W. Functional Analysis. International Series in Pure and Applied Mathematics. McGraw-Hill, Inc., New York, second edition, 1991.Google Scholar

Ryan, R. Boundary values of analytic vector valued functions. Indag. Math., 65:558–572, 1962.Google Scholar

Ryll, J. and Wojtaszczyk, P.. On homogeneous polynomials on a complex ball. Trans. Am. Math. Soc., 276(1):107–116, 1983.Google Scholar

Rzeszut, M. and Wojciechowski, M.. Independent sums of and . J. Funct. Anal., 273(2):836–873, 2017.Google Scholar

Sarason, D. Generalized interpolation in H^∞. Trans. Am. Math. Soc., 127:179–203, 1967.Google Scholar

Sawa, J. The best constant in the Khintchine inequality for complex Steinhaus variables, the case p = 1. Studia Math., 81(1):107–126, 1985.Google Scholar

Schachermayer, W., Sersouri, A., and Werner, E.. Moduli of nondentability and the Radon–Nikodým property in Banach spaces. Israel J. Math., 65(3):225–257, 1989.Google Scholar

Schwartz, L. Les applications p-sommantes. In Séminaire Maurey-Schwartz Année 1972–1973: Espaces L^p et applications radonifiantes, Exp. No. 2, page 19. Centre de Math., École Polytech., Paris, 1973.Google Scholar

Semenov, E. M. and Uksusov, S. N.. Multipliers of series in the Haar system. Sibirsk. Mat. Zh., 53(2):388–395, 2012.Google Scholar

Stegall, C. Optimization of functions on certain subsets of Banach spaces. Math. Ann., 236(2):171–176, 1978.Google Scholar

Stegall, C. Applications of Descriptive Topology in Functional Analysis. Institutsbericht 289. J. Kepler Universität, Institut für Mathematik, Linz, 1985.Google Scholar

Szarek, S. J. On the best constants in the Khinchin inequality. Studia Math., 58(2):197–208, 1976.Google Scholar

Talagrand, M. The three-space problem for L¹. J. Am. Math. Soc., 3(1):9–29, 1990.Google Scholar

Tsuji, M. Potential Theory in Modern Function Theory. Chelsea Publishing Co., New York, 1975.Google Scholar

Varopoulos, N. T. The Helson–Szegő theorem and A_p-functions for Brownian motion and several variables. J. Funct. Anal., 39(1):85–121, 1980.Google Scholar

Varopoulos, N. T. Probabilistic approach to some problems in complex analysis. Bull. Sci. Math. (2), 105(2):181–224, 1981.Google Scholar

Wark, H. M. A remark on the multipliers of the Haar basis of L¹[0, 1]. Studia Math., 227(2):141–148, 2015.Google Scholar

Wark, H. M. Operator-valued Fourier Haar multipliers on vector-valued L¹ spaces. J. Math. Anal. Appl., 450(2):1148–1156, 2017.Google Scholar

Weis, L. On the representation of order continuous operators by random measures. Trans. Am. Math. Soc., 285(2):535–563, 1984.Google Scholar

Weissler, F. B. Logarithmic Sobolev inequalities and hypercontractive estimates on the circle. J. Funct. Anal., 37(2):218–234, 1980.Google Scholar

Weisz, F. Martingale Hardy Spaces and their Applications in Fourier Analysis, volume 1568 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 1994.Google Scholar

Wojtaszczyk, P. Decompositions of Hp spaces. Duke Math. J., 46(3):635–644, 1979a.Google Scholar

Wojtaszczyk, P. On projections in spaces of bounded analytic functions with applications. Studia Math., 65(2):147–173, 1979b.Google Scholar

Wojtaszczyk, P. Projections and isomorphisms of the ball algebra. J. London Math. Soc. (2), 29(2):301–305, 1984.Google Scholar

Wojtaszczyk, P. Banach Spaces for Analysts, volume 25 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, Cambridge, 1991.Google Scholar

Wolniewicz, T. Seminar Notes. Arbeitsgruppe Funkionalanalysis. Institut f. Mathematik, J. Kepler University, Summer 1991.Google Scholar

Xu, Q. Littlewood–Paley theory for functions with values in uniformly convex spaces. J. Reine Angew. Math., 504:195–226, 1998.Google Scholar

Xu, Q. H. Inégalités pour les martingales de Hardy et renormage des espaces quasinormés. C. R. Acad. Sci. Paris Sér. I Math., 306(14):601–604, 1988.Google Scholar

Xu, Q. H. Applications du théorème de factorisation pour des fonctions à valeurs opérateurs. Studia Math., 95(3):273–292, 1990.Google Scholar

Xu, Q. H. Analytic functions with values in lattices and symmetric spaces of measurable operators. Math. Proc. Camb. Philos. Soc., 109(3):541–563, 1991.Google Scholar

Yudin, V. A. On the Fourier sums in L_p. Proc. Steklov Inst. Math., 180:279–280, 1989.Google Scholar

Zygmund, A. Trigonometric Series. Vol. I, II. Cambridge Mathematical Library. Cambridge University Press, Cambridge, 1988.Google Scholar