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arXiv · 2104.10733

Compactness of composition operators on the Bergman spaces of convex domains and analytic discs

Timothy G. Clos
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Abstract

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

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Timothy G. Clos. 2021-04-21. Compactness of composition operators on the Bergman spaces of convex domains and analytic discs. https://doi.org/10.1007/s10476-021-0094-6

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