On compactness of Hankel and the $\bar{\partial }$-Neumann operators on Hartogs domains in ${\mathbb{C}}^2$

Abstract

We prove that on smooth bounded pseudoconvex Hartogs domains in ${\mathbb{C}}^2$ compactness of the $\bar{\partial }$-Neumann operator is equivalent to compactness of all Hankel operators with symbols smooth on the closure of the domain.

10 pages, to appear in the Journal of Geometric Analysis

References in corpus (1)

• Compactness of the dbar-Neumann operator and commutators of the Bergman projection with continuous functions

Cited by in corpus (2)

• Compactness of Hankel operators with symbols continuous on the closure of pseudoconvex domains
• Schatten class Hankel and $\overline{\partial }$-Neumann operators on pseudoconvex domains in ${\mathbb{C}}^n$