Toeplitz operators on doubling Fock spaces

TL;DR

This paper investigates Toeplitz operators on doubling Fock spaces, providing characterizations of their boundedness, compactness, and Schatten class membership based on the properties of their symbols.

Contribution

It offers new criteria for Toeplitz operators on doubling Fock spaces, linking operator properties to measure-theoretic conditions of the symbols.

Findings

Characterization of bounded Toeplitz operators

Criteria for compactness of Toeplitz operators

Conditions for Schatten class membership

Abstract

We study Toeplitz operator theory on the doubling Fock spaces, which are Fock spaces whose exponential weight is associated to a subharmonic function with doubling Riesz measure. Namely, we characterize the boundedness, compactness and membership in the Schatten class of Toeplitz operators on doubling Fock spaces whose symbol is a positive Radon measure.