Characterizations of Hardy-Orlicz and Bergman-Orlicz spaces

被引：0
作者：
Dubtsov E.S. [1 ]
机构：
[1] St. Petersburg Department, Steklov Mathematical Institute, St. Petersburg
来源：
Journal of Mathematical Sciences | 2007年 / 141卷 / 5期
基金：
俄罗斯基础研究基金会;
关键词：
Holomorphic Function; Unit Ball; Hardy Space; Bergman Space; Orlicz Space;
D O I：
10.1007/s10958-007-0059-8
中图分类号：
学科分类号：
摘要：
Let ∇̃ and τ denote the invariant gradient and invariant measure on the unit ball B of ℂn, respectively. Assume that f is a holomorphic function on B and φ ∈ C2(ℝ) is a nonnegative, nondecreasing, convex function. Then f belongs to the Hardy-Orlicz space Hφ (B) if and only if ∫B φ″(log|f(z)|) |∇̃ f(z)|2/|f(z)|2(1 - |z|2)n dτ(z) < ∞. Analogous characterizations of Bergman-Orlicz spaces are obtained. Bibliography: 9 titles. © 2007 Springer Science+Business Media, Inc.
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收藏
页码：1531 / 1537
页数：6
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