Toeplitz operators on Bergman spaces induced by doubling weights in the unit ball of Cn

Abstract

In this paper, we study the boundedness and compactness of the Toeplitz operator $T_{\mu }:A_{\omega }^p\mapsto A_{\omega }^q$ for $1<p\le q$, where the weighted Bergman spaces $A_{\omega }^p$ are induced by (radially) doubling weights in the unit ball of $C^n$. The equivalence between the boundedness and compactness of $T_{\mu }:A_{\omega }^p\mapsto A_{\omega }^q$ is also established under the assumption with $1<q<p$. Our work extends the early work of Peláez, Rättyä, and Sierra to higher dimensions, as well as to a larger class of radial weights.