Essential norm and Schatten class of Hankel operators between 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 $h$.