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Schatten class Hankel operators on the Bergman spaces of strongly pseudoconvex domains


Author: Huiping Li
Journal: Proc. Amer. Math. Soc. 119 (1993), 1211-1221
MSC: Primary 47B35; Secondary 32A37, 47B10
MathSciNet review: 1169879
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Abstract: In this paper, we characterize holomorphic functions $ f$ such that the Hankel operators $ {H_{\bar f}}$ are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for $ p > 2n,\;{H_{\bar f}}$ is in the Schatten class $ {S_p}$ if and only if $ f$ is in the Besov space $ {B_p}$; for $ p \leqslant 2n,\;{H_{\bar f}}$ is in the Schatten class $ {S_p}$ if and only if $ f = {\text{constant}}$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1169879-9
Article copyright: © Copyright 1993 American Mathematical Society