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

Zeqian Chen; Wei Ouyang

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arXiv · 1005.2936

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

Zeqian Chen·Wei Ouyang

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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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Zeqian Chen, Wei Ouyang. 2013-08-21. Maximal and area integral characterizations of Bergman spaces in the unit ball of $\mathbb{C}^n$. https://arxiv.org/abs/1005.2936

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