Hostname: page-component-78c5997874-s2hrs Total loading time: 0 Render date: 2024-11-13T05:37:27.914Z Has data issue: false hasContentIssue false
  • English
  • Français

DIFFERENCES OF COMPOSITION OPERATORS BETWEEN WEIGHTED BERGMAN SPACES AND WEIGHTED BANACH SPACES OF HOLOMORPHIC FUNCTIONS

Published online by Cambridge University Press:  29 March 2010

ELKE WOLF
ELKE WOLF*
Affiliation:
Mathematical Institute, University of Paderborn, D-33095 Paderborn, Germany e-mail: lichte@math.uni-paderborn.de
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We characterise boundedness and compactness of differences of composition operators acting between weighted Bergman spaces Av, p and weighted Banach spaces H∞w of holomorphic functions defined on the open unit disk D.

Keywords

MSC 2000: 47B3347B38
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 52 , Issue 2 , May 2010 , pp. 325 - 332
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Bierstedt, K. D., Bonet, J. and Taskinen, J., Associated weights and spaces of holomorphic functions, Studia Math. 127 (1998), 137–168.CrossRefGoogle Scholar
2.Bonet, J., Domański, P. and Lindström, M., Essential norm and weak compactness of composition operators on weighted Banach spaces of analytic functions, Canad. Math. Bull. 42 (2) (1999), 139–148.CrossRefGoogle Scholar
3.Bonet, J., Domański, P., Lindström, M. and Taskinen, J., Composition operators between weighted Banach spaces of analytic functions, J. Aust. Math. Soc. (Serie A) 64 (1998), 101–118.CrossRefGoogle Scholar
4.Bonet, J., Friz, M. and Jordá, E., Composition operators between weighted inductive limits of spaces of holomorphic functions, Publ. Math. 67 (3-4) (2005), 333–348.Google Scholar
5.Bonet, J., Lindström, M. and Wolf, E., Differences of composition operators between weighted Banach spaces of holomorphic functions, J. Aust. Math. Soc. 84 (1) (2008), 9–20.CrossRefGoogle Scholar
6.Contreras, M. D. and Hernández-Díaz, A. G., Weighted composition operators in weighted Banach spaces of analytic functions, J. Aust. Math. Soc. (Serie A) 69 (2000), 41–60.CrossRefGoogle Scholar
7.Cowen, C. and MacCluer, B., Composition operators on spaces of analytic functions (CRC Press, Baca Raton, FL, 1995).Google Scholar
8.Domański, P. and Lindström, M., Sets of interpolation and sampling for weighted Banach spaces of holomorphic functions, Ann. Pol. Math. 79 (2002) 233–264.CrossRefGoogle Scholar
9.Duren, P. and Schuster, A., Bergman spaces, mathematical surveys and monographs 100 (American Mathematical Society, Providence, RI, 2004).CrossRefGoogle Scholar
10.Hedenmalm, H., Korenblum, B. and Zhu, K., Theory of Bergman Spaces, Graduate Texts in Mathematics 199 (Springer-Verlag, New York, 2000).CrossRefGoogle Scholar
11.Lindström, M. and Wolf, E., Essential norm of the difference of weighted composition operators, Monatsh. Math. 153 (2008), 133–143.CrossRefGoogle Scholar
12.Lusky, W., On weighted spaces of harmonic and holomorphic functions, J. Lond. Math. Soc. 51 (1995), 309–320.CrossRefGoogle Scholar
13.Moorhouse, J., Compact differences of composition operators, J. Funct. Anal. 219 (2005), 70–92.CrossRefGoogle Scholar
14.Nieminen, P., Compact differences of composition operators on Bloch and Lipschitz spaces, to appear in Comput. Methods Funct. Theory.Google Scholar
15.Shapiro, J. H., Composition operators and classical function theory (Springer, New York, 1993).CrossRefGoogle Scholar