Toeplitz Operators and Berezin-type Operators on Different Bergman Spaces

TL;DR

This paper investigates the properties of Toeplitz and Berezin-type operators on weighted Bergman spaces over tubular domains in complex space, focusing on their boundedness, compactness, and relation to Carleson measures.

Contribution

It provides new characterizations of boundedness and compactness for these operators on different Bergman spaces, linking them with Carleson measures.

Findings

Characterization of bounded Toeplitz and Berezin-type operators

Criteria for compactness in terms of Carleson measures

Connections established between operators and measure conditions

Abstract

In the present paper, we study the boundedness and compactness of Toeplitz operators and Berezin-type operators between different weighted Bergman spaces over tubular domains in $\mathbb{C}^n$. We establish their connection with Carleson measures and provide some characterizations.