Schatten Class Hankel Operators on Weighted Bergman Spaces induced by regular weights

TL;DR

This paper characterizes Schatten class Hankel operators on weighted Bergman spaces with regular weights using mean oscillation of symbols, combining classical methods with a new atomic decomposition approach.

Contribution

It introduces a novel atomic decomposition method to describe Schatten p-class Hankel operators on weighted Bergman spaces with regular weights.

Findings

Provides multiple characterizations of Schatten p-class Hankel operators.

Connects operator properties with mean oscillation of symbols.

Utilizes a new atomic decomposition technique for analysis.

Abstract

In this paper, for $1\leq p<\infty$, we provide several descriptions of Schatten $p$-class Hankel operators $H_f$ and $H_{\overline{f}}$ on the weight Bergman space $A^2_\omega$, in terms of a certain global and local mean oscillation of the symbol $f\in L^2_\omega$, provided $\omega$ is a class of regular weights. The approaches applied to rely on several classical methods, and simultaneously rely on a novel but more convenient construction associated with the atomic decomposition of $A^2_\omega$.