Schatten class Toeplitz operators acting on large weighted Bergman spaces

TL;DR

This paper characterizes when Toeplitz operators on large weighted Bergman spaces belong to Schatten classes, providing a comprehensive description of their membership criteria.

Contribution

It offers a complete characterization of Schatten class membership for Toeplitz operators on large weighted Bergman spaces, extending previous understanding.

Findings

Provides necessary and sufficient conditions for Schatten class membership.

Establishes a full description of the operator ideal membership.

Advances the theory of Toeplitz operators on weighted Bergman spaces.

Abstract

A full description of the membership in the Schatten ideal $S_ p(A^2_{\omega})$ for $0<p<\infty$ of the Toeplitz operator acting on large weighted Bergman spaces is obtained.