Schatten Class Hankel Operators on the Bergman Spaces of Strongly Pseudoconvex Domains

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 $f = {\text {constant}}$.