Compactness of composition operators on the Bergman space of bounded pseudoconvex domains in ${\mathbb{C}}^n$

Abstract

We study the compactness of composition operators on the Bergman spaces of certain bounded pseudoconvex domains in ${\mathbb{C}}^n$ with non-trivial analytic disks contained in the boundary. As a consequence we characterize that compactness of the composition operator with a holomorphic, continuous symbol (up to the closure) on the Bergman space of the polydisk.

7 pages