Localization of compactness of Hankel operators on pseudoconvex domains

Abstract

We prove the following localization for compactness of Hankel operators on Bergman spaces. Assume that D is a bounded pseudoconvex domain in C^n, p is a boundary point of D and B(p,r) is a ball centered at p with radius r so that U=D\cap B(p,r) is connected. We show that if the Hankel operator H^D_f is compact on A^2(D) (the symbols f is C^1 on the closure of D) then H^U_f is compact on A^2(U) where A^2(D) and A^2(U) denote the Bergman spaces on D and U, respectively.

9 pages. To appear in Illinois J. Math

References in corpus (2)

• Compactness of Hankel operators and analytic discs in the boundary of pseudoconvex domains
• On compactness of the dbar-Neumann problem and Hankel operators

Cited by in corpus (2)

• On compactness of Hankel and the $\bar{\partial }$-Neumann operators on Hartogs domains in ${\mathbb{C}}^2$
• Compactness of Hankel operators with symbols continuous on the closure of pseudoconvex domains