Essential norm and Schatten class of Hankel operators between weighted Fock spaces

TL;DR

This paper characterizes the essential norm and Schatten class membership of Hankel operators between weighted Fock and Lebesgue spaces, providing a comprehensive analysis of their boundedness and compactness properties.

Contribution

It offers new characterizations of the essential norm and Schatten class membership for Hankel operators on weighted Fock spaces, extending previous results to broader settings.

Findings

Explicit formulas for the essential norm of Hankel operators.

Criteria for Schatten-$h$ class membership of Hankel operators.

Applicable to all $1 \,\leq p, q < \infty$ in weighted Fock spaces.

Abstract

In this paper, we characterize the essential norm of Hankel operators from a weighted Fock space $F_{\varphi}^{p}$ to a weighted Lebesgue space $L_{\varphi}^{q}$ for all $1 \leq p, q < \infty$. Additionally, we characterize the Schatten-$h$ class membership for Hankel operators acting from $F_{\varphi}^{2}$ to $L_{\varphi}^{2}$, where the class is defined by a continuous increasing convex function $h$.