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arXiv · 2409.09529

Compactness of composition operators on the Bergman space of the bidisc

Timothy G. Clos·Zeljko Cuckovic·Sonmez Sahutoglu
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Abstract

Let $\varphi$ be a holomorphic self map of the bidisc that is Lipschitz on the closure. We show that the composition operator $C_{\varphi}$ is compact on the Bergman space if and only if $\varphi(\overline{\mathbb{D}^2})\cap \mathbb{T}^2=\emptyset$ and $\varphi(\overline{\mathbb{D}^2}\setminus \mathbb{T}^2)\cap b\mathbb{D}^2=\emptyset$.

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Timothy G. Clos, Zeljko Cuckovic, Sonmez Sahutoglu. 2024-09-14. Compactness of composition operators on the Bergman space of the bidisc. https://doi.org/10.1007/s00020-025-02808-8

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