Schatten Class Hankel Operators on Large Bergman spaces

TL;DR

This paper characterizes when Hankel operators with general symbols belong to Schatten classes on large Bergman spaces, extending previous results for the case p ≥ 1 to the range 0 < p < 1.

Contribution

It provides a complete characterization of Schatten class membership for Hankel operators on large Bergman spaces for p in (0,1), generalizing prior work.

Findings

Characterization of Hankel operators in Schatten classes for p in (0,1)

Extension of known results from p ≥ 1 to p in (0,1)

Advancement in understanding operator theory on large Bergman spaces

Abstract

We characterize the membership of Hankel operators with general symbols in the Schatten Classes $S^p,\, p\in(0,1),$ of the large Bergman spaces $A^2_{\omega}$. The case $p\geq 1$ was proved by Lin and Rochberg.