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

TL;DR

This paper introduces new generalized Bergman spaces on the unit ball in complex n-space, exploring properties of operators like projections and transforms, with potential applications in complex analysis.

Contribution

It defines and studies new holomorphic function spaces generalizing classical Bergman spaces, analyzing operator properties and integral representations.

Findings

Properties of Bergman-type projections established

Integral representations like Berezin transform characterized

Generalization of classical Bergman spaces demonstrated

Abstract

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.