Compactness of operators on the Bergman space of the Thullen domain

Abstract

We study compact operators on the Bergman space of the Thullen domain defined by $\{(z_1,z_2)\in {\mathbb{C}}^2:|z_1{|}^{2p}+|z_2{|}^2<1\}$ with $p>0$ and $p\ne 1$. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.

25 pages