Tent spaces and Littlewood-Paley $g$-functions associated with Bergman spaces in the unit ball of $\mathbb{C}^n$

Details Tent spaces and Littlewood-Paley $g$-functions associated with Bergman spaces in the unit ball of $\mathbb{C}^n$ Tent spaces and Littlewood-Paley $g$-functions associated with Bergman spaces in the unit ball of $\mathbb{C}^n$

2011-03-31

arxiv.org/abs/1103.6122v3

Mathematics

Functional Analysis

15 pages. Title changed, minor corrections

Scientific paper

In this paper, a family of holomorphic spaces of tent type in the unit ball of $\mathbb{C}^n$ is introduced, which is closely related to maximal and area integral functions in terms of the Bergman metric. It is shown that these spaces coincide with Bergman spaces. Furthermore, Littlewood-Paley type $g$-functions for the Bergman spaces are introduced in terms of the radial derivative, the complex gradient, and the invariant gradient. The corresponding characterizations for Bergman spaces are obtained as well. As an application, we obtain new maximal and area integral characterizations for Hardy-Sobolev spaces.

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