Journal of Operator Theory

Volume 83, Issue 2, Spring 2020 pp. 391-421.

Compactness of operators on the Bergman space of the Thullen domain

Authors: Zhenghui Huo (1), Brett D. Wick (2)
Author institution:(1) Department of Mathematics and Statistics, The University of Toledo, Toledo, OH 43606-3390, U.S.A.
(2) Department of Mathematics and Statistics, Washington University in St. Louis, St. Louis, MO 63130-4899, U.S.A.

Summary: We study compact operators on the Bergman space of the 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.

DOI: http://dx.doi.org/10.7900/jot.2018oct16.2216
Keywords: Bergman space, Toeplitz operator, compact operator, Thullen domain

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