BMO on Weighted Bergman Spaces over Tubular Domains

TL;DR

This paper characterizes BMO spaces and their relation to Hankel operators on weighted Bergman spaces over tubular domains, introduces a new projection operator, and provides integral representations for Bergman functions.

Contribution

It offers a novel characterization of Bloch spaces on tubular domains and establishes boundedness of a modified projection operator.

Findings

BMO spaces are characterized on tubular domains.

Boundedness of a new projection operator is proven.

Integral representations for Bergman functions are derived.

Abstract

In this paper, we characterize Bounded Mean Oscillation (BMO) and establish their connection with Hankel operators on weighted Bergman spaces over tubular domains. By utilizing the space BMO, we provide a new characterization of Bloch spaces on tubular domains. Next, we define a modified projection operator and prove its boundedness. Furthermore, we introduce differential operators and demonstrate that these operators belong to Lebesgue spaces on tubular domains. Finally, we establish an integral representation for Bergman functions using these differential operators.