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

Abstract

In this paper, we characterize holomorphic functions f f such that the Hankel operators H f ¯ {H_{\bar f}} are in the Schatten classes on bounded strongly pseudoconvex domains. It is proved that for p > 2 n , H f ¯ p > 2n,\;{H_{\bar f}} is in the Schatten class S p {S_p} if and only if f f is in the Besov space B p {B_p} ; for p ⩽ 2 n , H f ¯ p \leqslant 2n,\;{H_{\bar f}} is in the Schatten class S p {S_p} if and only if f = constant f = {\text {constant}} .