  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.
