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On Multipliers into Bergman Spaces and Nevanlinna Class

Published online by Cambridge University Press:  20 November 2018

P. Wojtaszczyk
P. Wojtaszczyk*
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, 00-950 Warszawa, Poland
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Abstract

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We use the general factorisation theorems of Grothendieck, Nikishin and Maurey to characterise coefficient multipliers between Bergman spaces and into the Nevanlinna class.

Keywords

30.B.1030.H.0546.E.15.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 33 , Issue 2 , 01 June 1990 , pp. 151 - 161
Copyright
Copyright © Canadian Mathematical Society 1990

References

1. [AS] Anderson, J. M. and Shields, A. L., Coefficient multipliers of Block functions, Trans. Amer. Math. Soc. 224 (1976), pp. 255–265.Google Scholar
2. [Bl] Bourgain, J., New Banach space properties of the disc algebra and HQQ, Acta Math. 152 (1984), pp 1–48.Google Scholar
3. [B2] Quelques propriétés linéaires topologiques de l'espace des series de Fourier uniformément convergentes, Séminaire Initiation à l'Analyse G. Choquet, M. Rogalski, J. Saint. Raymond (1982/83) exp. 14; also in CRAS (Paris) vol. 295 (1982) Série I, pp. 623-625.Google Scholar
4. [BST] Bennett, G., Stegenga, D. A. and Timoney, R. M., Coefficients of Block and Lipschitz functions, 111. J. Math. 25 No. 3 (1981), pp. 520–531.Google Scholar
5. [CW] Campbell, D. M. and Wickes, G. H., The Bloch-Nevanlinna conjecture revisited, Bull. Austr. Math. Soc. 18 (1978), pp. 447–453.Google Scholar
6. [D] Duren, P., Theory of Hp-spaces, Academic Press (1970).Google Scholar
7. [GR] Garcia-Cuerva, J. and Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North Holland Math. Studies 116 (1985).Google Scholar
8. [J] Jones, P. W., A complete, bounded, complex submanifold of C3, Proc. Amer. Math. Soc. 76 (1979), p. 305.Google Scholar
9. [K] Kranz, S. G., Holomorphic functions of bounded mean oscillation and mapping properties of the Szego kernel, Duke Math. J. 47 No. 4, pp. 743–761.Google Scholar
10. [LP1] Lindenstrauss, J. and Pelczynski, A., Absolutely summing operators in Lp-spaces and their applications, Studia Math. 29 (1968), pp. 275–326.Google Scholar
11. [LP2] Lindenstrauss, J. and Pelczynski, A., Contributions to the theory of the classical Banach spaces, J. Funct. Anal. 8 No. 2 (1971), pp. 225–249.Google Scholar
12. [M] Maurey, B., Théorèmes de factorisation pour les operateurs linéaires à valeurs dans les espaces Lp, Astérisque 11 (1974).Google Scholar
13. [N] Nikishin, E. M., Resonance theorems and superlinear operators, Uspekki Mat. Nauk 25 No. 6 (1970), pp. 129–191 (in Russian).Google Scholar
14. [R] Rolewicz, S., Metric Linear Spaces, Polish Scientific Publishers, Warszawa (1984).Google Scholar
15. [S] Stein, E. M., On limits of sequences of operators, Ann. of Math. 74 (1961), pp. 140–170.Google Scholar
16. [SW] Shields, A. L. and Williams, L., Bounded projections, duality and multipliers in spaces of analytic functions, Trans. Amer. Math. Soc. 162 (1971), pp. 287–302.Google Scholar