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arXiv · 1810.05899

Compactness of operators on the Bergman space of the Thullen domain

Zhenghui Huo·Brett D. Wick
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Abstract

We study compact operators on the Bergman space of the Thullen domain defined by $\{(z_1,z_2)\in \mathbb C^2: |z_1|^{2p}+|z_2|^2<1\}$ with $p>0$ and $p\neq 1$. The domain need not be smooth nor have a transitive automorphism group. We give a sufficient condition for the boundedness of various operators on the Bergman space. Under this boundedness condition, we characterize the compactness of operators on the Bergman space of the Thullen domain.

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Zhenghui Huo, Brett D. Wick. 2018-10-13. Compactness of operators on the Bergman space of the Thullen domain. https://arxiv.org/abs/1810.05899

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