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Maximal and area integral characterizations of Bergman spaces in the unit ball of $\mathbb{C}^n$

Authors
  • Chen, Zeqian
  • Ouyang, Wei
Type
Published Article
Publication Date
Aug 20, 2013
Submission Date
May 17, 2010
Source
arXiv
License
Yellow
External links

Abstract

In this paper, we present maximal and area integral characterizations of Bergman spaces in the unit ball of $\mathbb{C}^n.$ The characterizations are in terms of maximal functions and area integral functions on Bergman balls involving the radial derivative, the complex gradient, and the invariant gradient. As an application, we obtain new maximal and area integral characterizations of Besov spaces. Moreover, we give an atomic decomposition of real-variable type with respect to Carleson tubes for Bergman spaces.

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