Positive Toepltz operators on the Bergman space of a minimal bounded homogeneous domain

TL;DR

This paper characterizes when positive Toeplitz operators on the Bergman space of minimal bounded homogeneous domains are bounded or compact, using Berezin transform, averaging function, and Carleson property.

Contribution

It provides necessary and sufficient conditions for boundedness and compactness of positive Toeplitz operators in this setting, linking operator properties to function-theoretic criteria.

Findings

Characterization of bounded positive Toeplitz operators

Criteria for compactness of Toeplitz operators

Connection between operator properties and Carleson measures

Abstract

Necessary and sufficient conditions for positive Toeplitz operators on the Bergman space of a minimal bounded homogeneous domain to be bounded or compact are described in terms of the Berezin transform, the averaging function and the Carleson property.