Characterization of Schatten class Hankel operators on weighted Bergman spaces

Abstract

We completely characterize the simultaneous membership in the Schatten ideals $S_p$, $0<p<\infty$ of the Hankel operators $H_f$ and $H_{\bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function, proving a conjecture of Kehe Zhu from 1991.

V3

Cited by in corpus (3)

• Schatten class Hankel and $\overline{\partial }$-Neumann operators on pseudoconvex domains in ${\mathbb{C}}^n$
• On the compactness of Bergman-type integral operators
• Schatten Class Hankel Operators on Large Bergman spaces