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A characterization of weighted Bergman-Orlicz spaces on the unit ball in Cn

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 April 2009

Yasuo Matsugu  and
Jun Miyazawa
Jun Miyazawa
Affiliation:
Department of Mathematical Sciences Faculty of Science Shinshu University390–8621 MatsumotoJapan e-mail: matsugu@math.shinshu-u.ac.jp
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Abstract

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Let B denote the unit ball in Cn, and ν the normalized Lebesgue measure on B. For α > −1, define Here cα is a positive constant such that να(B) = 1. Let H(B) denote the space of all holomorphic functions in B. For a twice differentiable, nondecreasing, nonnegative strongly convex function ϕ on the real line R, define the Bergman-Orlicz space Aϕ(να) by

In this paper we prove that a function f ∈ H(B) is in Aϕ(να) if and only if where is the radial derivative of f.

MSC classification

Secondary: 32A36: Bergman spaces 32A35: $H^p$-spaces, Nevanlinna spaces 32A37: Other spaces of holomorphic functions (e.g. bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 1 , February 2003 , pp. 5 - 18
Copyright
Copyright © Australian Mathematical Society 2003

References

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