Berezin transform of Toeplitz operators on Bergman space with Bekolle and Bonami weights

TL;DR

This paper characterizes bounded and compact Toeplitz operators on weighted Bergman spaces with Bekolle-Bonami weights using Berezin transforms, supported by kernel estimates and Carleson properties.

Contribution

It provides a complete characterization of Toeplitz operators on these weighted spaces in terms of Berezin transforms, advancing understanding of their boundedness and compactness.

Findings

Complete characterization of Toeplitz operators via Berezin transforms

Kernel estimates and Carleson properties are crucial for analysis

Results apply to weighted Bergman spaces with Bekolle-Bonami weights

Abstract

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We completely characterized every case of the bounded and compact Toeplitz operators on the weighted Bergman spaces with B\'{e}koll\'{e}-Bonami weights in terms of Berezin transforms.