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

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.

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