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arXiv · 1902.07681

Compactness and Singular Points of Composition Operators on Bergman spaces

Timothy G. Clos
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Abstract

Let $\Omega\subset \mathbb{C}^n$ for $n\geq 2$ be a bounded pseudoconvex domain with a $C^2$-smooth boundary. We study the compactness of composition operators on the Bergman spaces of smoothly bounded convex domains. We give a partial characterization of compactness of the composition operator (with sufficient regularity of the symbol) in terms of the behavior of the Jacobian on the boundary. We then construct a counterexample to show the converse of the theorem is false.

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Timothy G. Clos. 2019-02-20. Compactness and Singular Points of Composition Operators on Bergman spaces. https://arxiv.org/abs/1902.07681

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