Toeplitz Operators with Positive Measures on Harmonic Fock Spaces

TL;DR

This paper investigates Toeplitz operators with positive measures on harmonic Fock spaces, establishing criteria for their boundedness, compactness, and Schatten class membership using Berezin transform techniques.

Contribution

It provides new characterizations of Toeplitz operators on harmonic Fock spaces, linking their properties to Berezin transforms and measure conditions.

Findings

Characterization of bounded Toeplitz operators via Berezin transform

Criteria for compactness of Toeplitz operators

Conditions for Schatten class membership

Abstract

In this paper, we study the basic properties of Toeplitz Operators with positive measures $\mu$ on harmonic Fock spaces. We prove equivalent conditions for boundedness, compactness and Schatten classes $S_{p}$ of $T_{\mu}$ by using the methods of Berezin transform of operators.