Toeplitz operators on Bergman spaces with exponential weights

Abstract

In this paper, we focus on the weighted Bergman spaces $A_{\phi }^p$ in $\mathbb{D}$ with $\phi \in {\mathcal{W}}_0$. We first give characterizations of those finite positive Borel measures $\mu$ in $\mathbb{D}$ such that the embedding $A_{\phi }^p\subset L_{\mu }^q$ is bounded or compact for $0<p,q<\infty$. Then we describe bounded or compact Toeplitz operators $T_{\mu }$ from one Bergman space $A_{\phi }^p$ to another $A_{\phi }^q$ for all possible $0<p,q<\infty$. Finally, we characterize Schatten class Toeplitz operators on $A_{\phi }^2$.

26 pages