Toeplitz operators on weighted Fock spaces with $A_{\infty}$-type weights

TL;DR

This paper characterizes bounded, compact, and Schatten class Toeplitz operators with positive measure symbols on weighted Fock spaces with $A_{ infty}$-type weights, using kernel estimates and exploring applications to other operators.

Contribution

It provides a new characterization of Toeplitz operators on weighted Fock spaces with $A_{ infty}$-type weights, including Schatten class criteria.

Findings

Characterization of Toeplitz operators with positive measure symbols

Criteria for boundedness, compactness, and Schatten class membership

Applications to Volterra and weighted composition operators

Abstract

By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight on the complex plane satisfying an $A_{\infty}$-type condition. Applications to Volterra operators and weighted composition operators are given.