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Composition operators on weighted Bergman-Orlicz spaces

Published online by Cambridge University Press:  17 April 2009

Ajay K. Sharma  and
S. D. Sharma
Ajay K. Sharma
Affiliation:
Department of Applied Physics and Mathematics, Shri Mata Vaishno Devi University, Jammu–180006, India, e-mail: [email protected]
S. D. Sharma
Affiliation:
Department of Mathematics, University of Jammu, Jammu–180006, India, e-mail: [email protected]
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In this paper, composition operators acting on Bergman-Orlicz spaces

are studied, where ψ is a non-constant, non-decreasing convex function defined on (-∞, ∞) which satisfies the growth condition . In fact, under a mild condition on ∞, we show that every holomorphic-self map ∞ of induces a bounded composition operator on and C∞ is compact on if and only if it is compact on .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 75 , Issue 2 , April 2007 , pp. 273 - 287
Copyright
Copyright © Australian Mathematical Society 2007

References

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