Toeplitz operators and Hankel operators on a Bergman space with an exponential weight on the unit ball

Abstract

We consider the weighted Bergman space \(A^2_\psi \) of all holomorphic functions on \({\textbf{B}_n}\) square integrable with respect to an exponential weight measure \(e^{-{\psi }} dV\) on \({\textbf{B}_n}\), where

$$\begin{aligned} \psi (z):=\frac{1}{1-|z|^2}. \end{aligned}$$

We characterize boundedness (or compactness) of Toeplitz operators and Hankel operators on \(A^2_\psi \).