A Theorem of Nehari Type on the Bergman Space

Abstract

In this paper we concern with the characterization of bounded linear operators $S$ acting on the weighted Bergman spaces on the unit ball. It is shown that, if $S$ satisfies the commutation relation $ST_{z_i} = T_{\overline{z}_i}S(i = 1, · · · , n)$, where $T_{z_i} = z_if$ and $T_{\overline{z}_i} = P(\overline{z}_if)$ where $P$ is the weighted Bergman projection, then $S$ must be a Hankel operator.