Hilbert-Schmidt Hankel operators over semi-Reinhardt domains

Abstract

Let $\Omega$ be an arbitrary bounded semi-Reinhardt domain in ${\mathbb{C}}^{m+n}$. We show that for $m\ge 2$, if a Hankel operator with an anti-holomorphic symbol is Hilbert-Schmidt on the Bergman space $L_a^2(\Omega )$, then it must equal zero. This fact has previously been proved for Reinhardt domains.

This paper has been withdrawn by the authors due to mistake in the proof of Main theorem