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

Li, Huiping

doi:10.1090/S0002-9939-1993-1169879-9

Schatten class Hankel operators on the Bergman spaces of strongly pseudoconvex domains
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Proc. Amer. Math. Soc. 119 (1993), 1211-1221 Request permission

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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