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

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

2010-05-17

arxiv.org/abs/1005.2936v4

Mathematics

Functional Analysis

25 pages

Scientific paper

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. A special case of this is new characterizations of Hardy-Sobolev spaces involving maximal and area integral functions defined on Bergman balls in the unit ball of $\mathbb{C}^n.$ Moreover, we give a real-variable atomic decomposition of Bergman spaces with respect to Carleson tubes.

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