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On Multipliers into Bergman Spaces and Nevanlinna Class

Published online by Cambridge University Press:  20 November 2018

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.

Type
Research Article
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. 255265.Google Scholar
2. [Bl] Bourgain, J., New Banach space properties of the disc algebra and HQQ, Acta Math. 152 (1984), pp 148.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. 520531.Google Scholar
5. [CW] Campbell, D. M. and Wickes, G. H., The Bloch-Nevanlinna conjecture revisited, Bull. Austr. Math. Soc. 18 (1978), pp. 447453.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. 743761.Google Scholar
10. [LP1] Lindenstrauss, J. and Pelczynski, A., Absolutely summing operators in Lp-spaces and their applications, Studia Math. 29 (1968), pp. 275326.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. 225249.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. 129191 (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. 140170.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. 287302.Google Scholar