Real-variable characterizations of Bergman spaces in the unit ball of $\mathbb{C}^n$

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 functions and area 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 real-variable characterizations for Hardy-Sobolev spaces.