Compactness of Hankel operators with symbols continuous on the closure of pseudoconvex domains

Abstract

Let $\Omega$ be a bounded pseudoconvex domain in ${\mathbb{C}}^2$ with Lipschitz boundary or a bounded convex domain in ${\mathbb{C}}^n$ and $\varphi \in C(\overline{\Omega })$ such that $H_{\varphi }$ is compact on $A^2(\Omega )$. Then $\varphi \circ f$ is holomorphic for any holomorphic $f:\mathbb{D}\to b\Omega$.

made minor changes. To appear in Integral Equations Operator Theory