[1] Adams, D. R., and Hedberg, L. I. 1996. Function Spaces and Potential Theory. Grundlehren der Mathematischen Wissenschaften, vol. 314. Berlin: Springer-Verlag.
[2] Agler, J. 1988. Some interpolation theorems of Nevanlinna-Pick type. Unpublished manuscript.
[3] Agler, J. 1990. A disconjugacy theorem for Toeplitz operators. Amer. J. Math., 112(1), 1–14.
[4] Agler, J., and McCarthy, J. E. 2002. Pick Interpolation and Hilbert Function Spaces. Graduate Studies in Mathematics, vol. 44. Providence, RI: American Mathematical Society.
[5] Ahlfors, L. V. 1973. Conformai Invariants: Topics in Geometric Function Theory. McGraw-Hill Series in Higher Mathematics. New York: McGraw-Hill.
[6] Aikawa, H., and Essen, M. 1996. Potential Theory—Selected Topics. Lecture Notes in Mathematics, vol. 1633. Berlin: Springer-Verlag.
[7] Aleman, A. 1993. The multiplication operator on Hilbert spaces of analytic functions. Habilitationsschrift, Fern Universität, Hagen.
[8] Arazy, J., and Fisher, S. D. 1985. The uniqueness of the Dirichlet space among Mobius-invariant Hilbert spaces. Illinois J. Math., 29(3), 449–462.
[9] Arcozzi, N., Rochberg, R., and Sawyer, E. T. 2002. Carleson measures for analytic Besov spaces. Rev. Mat. Iberoamericana, 18(2), 443–510.
[10] Arcozzi, N., Rochberg, R., and Sawyer, E. T. 2008. Carleson measures for the Drury-Arveson Hardy space and other Besov-Sobolev spaces on complex balls. Adv. Math., 218(4), 1107–1180.
[11] Arcozzi, N., Rochberg, R., Sawyer, E. T., and Wick, B. D. 2011. The Dirichlet space: a survey. New York J. Math., 17A, 45–86.
[12] Armitage, D. H., and Gardiner, S. J. 2001. Classical Potential Theory. Springer Monographs in Mathematics. London: Springer-Verlag.
[13] Bénéteau, C., Condori, A., Liaw, C., Seco, D., and Sola, A.Cyclicity in Dirichlet-type spaces and extremal polynomials. J. Anal. Math. To appear.
[14] Berenstein, C. A., and Gay, R. 1991. Complex Variables. Graduate Texts in Mathematics, vol. 125. New York: Springer-Verlag.
[15] Beurling, A. 1933. Etudes sur un problème de majoration. Doctoral thesis, Uppsala University.
[16] Beurling, A. 1940. Ensembles exceptionnels. Acta Math., 72, 1–13.
[17] Bishop, C. J. 1994. Interpolating sequences for the Dirichlet space and its multipliers. Unpublished manuscript.
[18] Bøe, B. 2005. An interpolation theorem for Hilbert spaces with Nevanlinna-Pick kernel. Proc. Amer. Math. Soc., 133(7), 2077–2081.
[19] Bogdan, K. 1996. On the zeros of functions with finite Dirichlet integral. Kodai Math. J., 19(1), 7–16.
[20] Borichev, A. 1993. A note on Dirichlet-type spaces. Uppsala University Department of Mathematics Report 11.
[21] Borichev, A. 1994. Boundary behavior in Dirichlet-type spaces. Uppsala University Department of Mathematics Report 3.
[22] Bourdon, P. S. 1986. Cellular-indecomposable operators and Beurling's theorem. Michigan Math J., 33(2), 187–193.
[23] Brown, L., and Cohn, W. 1985. Some examples of cyclic vectors in the Dirichlet space. Proc. Amer. Math. Soc., 95(1), 42–46.
[24] Brown, L., and Shields, A. L. 1984. Cyclic vectors in the Dirichlet space. Trans. Amer. Math. Soc., 285(1), 269–303.
[25] Carleson, L. 1952a. On the zeros of functions with bounded Dirichlet integrals. Math. Z., 56, 289–295.
[26] Carleson, L. 1952b. Sets of uniqueness for functions regular in the unit circle. Acta Math., 87, 325–345.
[27] Carleson, L. 1960. A representation formula for the Dirichlet integral. Math. Z., 73, 190–196.
[28] Carleson, L. 1962. Interpolations by bounded analytic functions and the corona problem. Ann. Math. (2), 76, 547–559.
[29] Carleson, L. 1967. Selected Problems on Exceptional Sets. Van Nostrand Mathematical Studies, No. 13. Princeton, NJ: Van Nostrand.
[30] Carlsson, M. 2008. On the Cowen-Douglas class for Banach space operators. Integral Equations Operator Theory, 61(4), 593–598.
[31] Caughran, J. G. 1969. Two results concerning the zeros of functions with finite Dirichlet integral. Canad. J. Math., 21, 312–316.
[32] Caughran, J. G. 1970. Zeros of analytic functions with infinitely differentiable boundary values. Proc. Amer. Math. Soc., 24, 700–704.
[33] Chacón, G. R. 2011. Carleson measures on Dirichlet-type spaces. Proc. Amer. Math. Soc., 139(5), 1605–1615.
[34] Chang, S.-Y. A., and Marshall, D. E. 1985. On a sharp inequality concerning the Dirichlet integral. Amer. J. Math., 107(5), 1015–1033.
[35] Chartrand, R. 2002. Toeplitz operators on Dirichlet-type spaces. J. Operator Theory, 48(1), 3–13.
[36] Cowen, C. C., and MacCluer, B. D. 1995. Composition Operators on Spaces of Analytic Functions. Studies in Advanced Mathematics. Boca Raton, FL: CRC Press.
[37] Cowen, M. J., and Douglas, R. G. 1978. Complex geometry and operator theory. Acta Math., 141(3–4), 187–261.
[38] Doob, J. L. 1984. Classical Potential Theory and its Probabilistic Counterpart. Grundlehren der Mathematischen Wissenschaften, vol. 262. New York: Springer-Verlag.
[39] Douglas, J. 1931. Solution of the problem of Plateau. Trans. Amer. Math. Soc., 33(1), 263–321.
[40] Duren, P. L. 1970. Theory of Hp Spaces. Pure and Applied Mathematics, Vol. 38. New York: Academic Press.
[41] Dyn′kin, E. M. 1972. Extensions and integral representations of smooth functions of one complex variable. Dissertation, Leningrad.
[42] El-Fallah, O., Kellay, K., Mashreghi, J., and Ransford, T.One-box conditions for Carleson measures for the Dirichlet space. Proc. Amer. Math. Soc. To appear.
[43] El-Fallah, O., Kellay, K., and Ransford, T. 2006. Cyclicity in the Dirichlet space. Ark. Mat., 44(1), 61–86.
[44] El-Fallah, O., Kellay, K., and Ransford, T. 2009. On the Brown-Shields conjecture for cyclicity in the Dirichlet space. Adv. Math., 222(6), 2196–2214.
[45] El-Fallah, O., Kellay, K., Shabankhah, M., and Youssfi, H. 2011. Level sets and composition operators on the Dirichlet space. J. Funct. Anal., 260(6), 1721–1733.
[46] El-Fallah, O., Kellay, K., Mashreghi, J., and Ransford, T. 2012. A self-contained proof of the strong-type capacitary inequality for the Dirichlet space. Pages 1–20 of: Complex Analysis and Potential Theory. CRM Proc. Lecture Notes, vol. 55. Providence, RI: American Mathematical Society.
[47] Essén, M. 1987. Sharp estimates of uniform harmonic majorants in the plane. Ark. Mat., 25(1), 15–28.
[48] Frostman, O. 1935. Potentiel d'équilibre et capacité des ensembles avec quelques applications à la théorie des fonctions. Thesis. Meddel. Lunds Univ. Mat. Sem., 3, 1–118.
[49] Gallardo-Gutiérrez, E. A., and González, M. J. 2003. Exceptional sets and Hilbert-Schmidt composition operators. J. Funct. Anal., 199(2), 287–300.
[50] Garnett, J. B. 2007. Bounded Analytic Functions. revised first edn. Graduate Texts in Mathematics, vol. 236. New York: Springer.
[51] Garnett, J. B., and Marshall, D. E. 2005. Harmonic Measure. New Mathematical Monographs, vol. 2. Cambridge: Cambridge University Press.
[52] Guillot, D. 2012a. Blaschke condition andzero sets in weighted Dirichlet spaces. Ark. Mat., 50(2), 269–278.
[53] Guillot, D. 2012b. Fine boundary behavior and invariant subspaces of harmonically weighted Dirichlet spaces. Complex Anal. Operator Theory, 6(6), 1211–1230.
[54] Hansson, K. 1979. Imbedding theorems of Sobolev type in potential theory. Math. Scand., 45(1), 77–102.
[55] Hardy, G. H. 1949. Divergent Series. Oxford: Clarendon Press.
[56] Hastings, W. W. 1975. A Carleson measure theorem for Bergman spaces. Proc. Amer. Math. Soc., 52, 237–241.
[57] Hayman, W. K., and Kennedy, P. B. 1976. Subharmonic Functions, vol. 1. London Mathematical Society Monographs, No. 9. London: Academic Press [Harcourt Brace Jovanovich Publishers].
[58] Hedenmalm, H., and Shields, A. L. 1990. Invariant subspaces in Banach spaces of analytic functions. Michigan Math. J., 37(1), 91–104.
[59] Helms, L. L. 1975. Introduction to Potential Theory. Pure and Applied Mathematics, vol. 22. Huntington, NY: Robert E. Krieger.
[60] Hille, E. 1962. Analytic Function Theory, vol. II. Introductions to Higher Mathematics. Boston, MA: Ginn and Co.
[61] Kahane, J.-P., and Salem, R. 1994. Ensembles parfaits et séries trigono-métriques. Second edn. Paris: Hermann.
[62] Kellay, K. 2011. Poincaré type inequality for Dirichlet spaces and application to the uniqueness set. Math. Scand., 108(1), 103–114.
[63] Kellay, K., and Mashreghi, J. 2012. On zero sets in the Dirichlet space. J. Geom. Anal., 22(4), 1055–1070.
[64] Kerman, R., and Sawyer, E. T. 1988. Carleson measures and multipliers of Dirichlet-type spaces. Trans. Amer. Math. Soc., 309(1), 87–98.
[65] Koosis, P. 1992. The Logarithmic Integral II. Cambridge Studies in Advanced Mathematics, vol. 21. Cambridge: Cambridge University Press.
[66] Koosis, P. 1998. Introduction to Hp Spaces. Second edn. Cambridge Tracts in Mathematics, vol. 115. Cambridge: Cambridge University Press.
[67] Korenblum, B. I. 1972. Invariant subspaces of the shift operator in a weighted Hilbert space. Math. USSR-Sb., 18, 111–138.
[68] Korenblum, B. I. 2006. Blaschke sets for Bergman spaces. Pages 145–152 of: Bergman Spaces and Related Topics in Complex Analysis. Contemp. Math., vol. 404. Providence, RI: American Mathematical Society.
[69] Korolevič, V. S. 1970. A certain theorem of Beurling and Carleson. Ukrainian Math. J., 22(6), 710–714.
[70] Landkof, N. S. 1972. Foundations of Modern Potential Theory. Grundlehren der mathematischen Wissenschaften, vol. 180. New York: Springer-Verlag.
[71] Lefèvre, P., Li, D., Queffélec, H., and Rodríguez-Piazza, L. 2013. Compact composition operators on the Dirichlet space and capacity of sets of contact points. J. Funct. Anal., 264(4), 895–919.
[72] Luecking, D. H. 1987. Trace ideal criteria for Toeplitz operators. J. Funct. Anal., 73(2), 345–368.
[73] MacCluer, B. D., and Shapiro, J. H. 1986. Angular derivatives and compact composition operators on the Hardy and Bergman spaces. Canad. J. Math., 38(4), 878–906.
[74] Malliavin, P. 1977. Sur l'analyse harmonique de certaines classes de séries de Taylor. Pages 71–91 of: Symposia Mathematica, Vol. XXII (Convegno sull'Analisi Armonica e Spazi di Funzioni su Gruppi Localmente Compatti, IN-DAM, Rome, 1976). London: Academic Press.
[75] Marshall, D. E. 1989. A new proof of a sharp inequality concerning the Dirichlet integral. Ark. Mat., 27(1), 131–137.
[76] Marshall, D. E., and Sundberg, C. 1989. Interpolating sequences for the multipliers ofthe Dirichlet space. Unpublished manuscript.
[77] Mashreghi, J. 2009. Representation Theorems in Hardy Spaces. London Mathematical Society Student Texts, vol. 74. Cambridge: Cambridge University Press.
[78] Mashreghi, J., Ransford, T., and Shabankhah, M. 2010. Arguments of zero sets in the Dirichlet space. Pages 143–148 of: Hilbert Spaces ofAnalytic Functions. CRM Proc. Lecture Notes, vol. 51. Providence, RI: American Mathematical Society.
[79] Maz′ya, V. G., and Havin, V. P. 1973. Application of the (p, l)-capacity to certain problems of the theory of exceptional sets. Mat. Sb. (N.S.), 90(132), 558–591, 640.
[80] Meyers, N. G. 1970. A theory of capacities for potentials of functions in Lebesgue classes. Math. Scand., 26, 255–292 (1971).
[81] Monterie, M. A. 1997. Capacities of certain Cantor sets. Indag. Math. (N.S.), 8(2), 247–266.
[82] Nagel, A., and Stein, E. M. 1984. On certain maximal functions and approach regions. Adv. Math., 54(1), 83–106.
[83] Nagel, A., Rudin, W., and Shapiro, J. H. 1982. Tangential boundary behavior of functions in Dirichlet-type spaces. Ann. Math. (2), 116(2), 331–360.
[84] Nagel, A., Rudin, W., and Shapiro, J. H. 1983. Tangential boundary behavior of harmonic extensions of Lp potentials. Pages 533–548 of: Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, IL, 1981). Wadsworth Math. Ser. Belmont, CA: Wadsworth.
[85] Nehari, Z. 1975. Conformai Mapping. New York: Dover Publications.
[86] Novinger, W. P. 1971. Holomorphic functions with infinitely differentiable boundary values. Illinois J. Math., 15, 80–90.
[87] Ohtsuka, M. 1957. Capacité d'ensembles de Cantor généralisés. Nagoya Math. J., 11, 151–160.
[88] Olin, R. F., and Thomson, J. E. 1984. Cellular-indecomposable subnormal operators. Integral Equations Operator Theory, 7(3), 392–430.
[89] Parrott, S. 1978. On a quotient norm and the Sz.-Nagy–Foia lifting theorem. J. Funct. Anal., 30(3), 311–328.
[90] Peller, V. V., and Hruscev, S. V. 1982. Hankel operators, best approximations and stationary Gaussian processes. Russian Math. Surveys, 37(1), 61–144.
[91] Pommerenke, Ch. 1975. Univalent Functions. Göttingen: Vandenhoeck & Ruprecht.
[92] Pommerenke, Ch. 1992. Boundary Behaviour ofConformal Maps. Grundlehren der Mathematischen Wissenschaften, vol. 299. Berlin: Springer-Verlag.
[93] Ransford, T. 1995. Potential Theory in the Complex Plane. London Mathematical Society Student Texts, vol. 28. Cambridge: Cambridge University Press.
[94] Ransford, T., and Selezneff, A. 2012. Capacity and covering numbers. Potential Anal., 36, 223–233.
[95] Richter, S. 1988. Invariant subspaces of the Dirichlet shift. J. Reine Angew. Math., 386, 205–220.
[96] Richter, S. 1991. A representation theorem for cyclic analytic two-isometries. Trans. Amer. Math. Soc., 328(1), 325–349.
[97] Richter, S., and Shields, A. L. 1988. Bounded analytic functions in the Dirichlet space. Math. Z., 198(2), 151–159.
[98] Richter, S., and Sundberg, C. 1991. A formula for the local Dirichlet integral. Michigan Math. J., 38(3), 355–379.
[99] Richter, S., and Sundberg, C. 1992. Multipliers and invariant subspaces in the Dirichlet space. J. Operator Theory, 28(1), 167–186.
[100] Richter, S., and Sundberg, C. 1994. Invariant subspaces of the Dirichlet shift and pseudocontinuations. Trans. Amer. Math. Soc., 341(2), 863–879.
[101] Richter, S., Ross, W. T., and Sundberg, C. 2004. Zeros of functions with finite Dirichlet integral. Proc. Amer. Math. Soc., 132(8), 2361–2365.
[102] Rochberg, R., and Wu, Z. J. 1992. Toeplitz operators on Dirichlet spaces. Integral Equations Operator Theory, 15(2), 325–342.
[103] Ross, W. T. 2006. The classical Dirichlet space. Pages 171–197 of: Recent Advances in Operator-Related Function Theory. Contemp. Math., vol. 393. Providence, RI: American Mathematical Society.
[104] Rudin, W. 1987. Real and Complex Analysis. Third edn. New York: McGraw-Hill.
[105] Rudin, W. 1992. Power series with zero-sum on countable sets. Complex Variables Theory Appl., 18(3–4), 283–284.
[106] Saff, E. B., and Totik, V. 1997. Logarithmic Potentials with External Fields. Grundlehren der Mathematischen Wissenschaften, vol. 316. Berlin: Springer-Verlag.
[107] Sarason, D. 1986. Doubly shift-invariant spaces in H2. J. Operator Theory, 16(1), 75–97.
[108] Sarason, D. 1997. Local Dirichlet spaces as de Branges-Rovnyak spaces. Proc. Amer. Math. Soc., 125(7), 2133–2139.
[109] Seip, K. 2004. Interpolation and Sampling in Spaces of Analytic Functions. University Lecture Series, vol. 33. Providence, RI: American Mathematical Society.
[110] Shapiro, H. S., and Shields, A. L. 1962. On the zeros of functions with finite Dirichlet integral and some related function spaces. Math. Z., 80, 217–229.
[111] Shapiro, J. H. 1980. Cauchy transforms and Beurling-Carleson-Hayman thin sets. Michigan Math. J., 27(3), 339–351.
[112] Shapiro, J. H. 1987. The essential norm of a composition operator. Ann. Math. (2), 125(2), 375–404.
[113] Shapiro, J. H. 1993. Composition Operators and Classical Function Theory. Universitext: Tracts in Mathematics. New York: Springer-Verlag.
[114] Shields, A. L. 1983. An analogue of the Fejér-Riesz theorem for the Dirichlet space. Pages 810–820 of: Conference on Harmonic Analysis in Honor of Antoni Zygmund, Vol. I, II (Chicago, IL, 1981). Wadsworth Math. Ser. Belmont, CA: Wadsworth.
[115] Shimorin, S. M. 1998. Reproducing kernels and extremal functions in Dirichlet-type spaces. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 255 (Issled. po Linein. Oper. i Teor. Funkts. 26), 198–220, 254. Translation in J. Math. Sci. (New York) 107(4) (2001), 4108–4124.
[116] Shimorin, S. M. 2002. Complete Nevanlinna-Pick property of Dirichlet-type spaces. J. Funct. Anal., 191(2), 276–296.
[117] Stegenga, D. A. 1980. Multipliers of the Dirichlet space. Illinois J. Math., 24(1), 113–139.
[118] Taylor, B. A., and Williams, D. L. 1970. Ideals in rings of analytic functions with smooth boundary values. Canad. J. Math., 22, 1266–1283.
[119] Taylor, G. D. 1966. Multipliers on Dα. Trans. Amer. Math. Soc., 123, 229–240.
[120] Tsuji, M. 1975. Potential Theory in Modern Function Theory. New York: Chelsea.
[121] Twomey, J. B. 1989. Tangential limits for certain classes of analytic functions. Mathematika, 36(1), 39–49.
[122] Twomey, J. B. 2002. Tangential boundary behaviour of harmonic and holomorphic functions. J. London Math. Soc. (2), 65(1), 68–84.
[123] Wojtaszczyk, P. 1991. Banach Spaces for Analysts. Cambridge Studies in Advanced Mathematics, vol. 25. Cambridge: Cambridge University Press.
[124] Wynn, A. 2011. Sufficient conditions for weighted admissibility of operators with applications to Carleson measures and multipliers. Q. J. Math., 62(3), 747–770.