Modified Bergman spaces on the unit ball of ${\mathbb{C}}^n$ and applications

In this paper, we introduce new spaces of holomorphic functions on the unit ball ${\mathbb{B}}_n$ of ${\mathbb{C}}^n$ generalizing the classical Bergman spaces. The main results include the properties of some operators and integrals representations such as Bergman-type projections, and Berezin transform.