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

TL;DR

This paper introduces tent spaces related to Bergman spaces in the unit ball of c4a3^n, establishes their equivalence, and develops Littlewood-Paley g-functions for characterizations, also applying results to Hardy-Sobolev spaces.

Contribution

It defines new tent spaces associated with Bergman spaces and provides novel Littlewood-Paley g-function characterizations, extending understanding of these function spaces.

Findings

Tent spaces coincide with Bergman spaces.

New Littlewood-Paley g-function characterizations are established.

Applications to Hardy-Sobolev spaces are demonstrated.

Abstract

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.