Compactness of Hankel operators with continuous symbols

Abstract

Let $\Omega$ be a bounded convex Reinhardt domain in ${\mathbb{C}}^2$ and $\varphi \in C(\bar{\Omega })$. We show that the Hankel operator $H_{\varphi }$ is compact if and only if $\varphi$ is holomorphic along every non-trivial analytic disc in the boundary of $\Omega$.

some minor changes; to appear in Complex Anal. Oper. Theory

Cited by in corpus (5)

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• On spectra of Hankel operators on the polydisc
• Compactness of composition operators on the Bergman spaces of convex domains and analytic discs