Zero products of Toeplitz operators on Reinhardt domains

Abstract

Let $\Omega$ be a bounded Reinhardt domain in ${\mathbb{C}}^n$ and ${\varphi }_1,\dots ,{\varphi }_m$ be finite sums of bounded quasi-homogeneous functions. We show that if the product of Toeplitz operators $T_{{\varphi }_m}\cdots T_{{\varphi }_1}=0$ on the Bergman space on $\Omega$, then ${\varphi }_j=0$ for some $j$.

to appear in Can. Math. Bull., 11 pages