Hilbert-Schmidt Hankel operators with harmonic symbols on the Bergman space of strongly pseudoconvex domains in $\mathbb{C}^n$

Abstract

We characterize Hilbert-Schmidt Hankel operators on the Bergman spaces of smooth bounded strongly pseudoconvex domains in $\mathbb{C}^n$ for $n \geq 2$. We consider harmonic symbols of class $C^3$ up to the closure of the domain and show $H_ϕ$ is Hilbert-Schmidt if and only if $ϕ$ is holomorphic on the domain.