Open Access
Fall 2012 Localization of compactness of Hankel operators on pseudoconvex domains
Sönmez Şahutoğlu
Illinois J. Math. 56(3): 795-804 (Fall 2012). DOI: 10.1215/ijm/1391178548

Abstract

We prove the following localization for compactness of Hankel operators on Bergman spaces. Assume that $\Omega $ is a bounded pseudoconvex domain in $\mathbb{C} ^{n}$, $p$ is a boundary point of $\Omega $, and $B(p,r)$ is a ball centered at $p$ with radius $r$ so that $U=\Omega \cap B(p,r)$ is connected. We show that if the Hankel operator $H^{\Omega }_{\phi}$ with symbol $\phi\in C^{1}(\overline{\Omega } )$ is compact on $A^{2}(\Omega )$ then $H^{U}_{R_{U}(\phi)}$ is compact on $A^{2}(U)$ where $R_{U}$ denotes the restriction operator on $U$, and $A^{2}(\Omega )$ and $A^{2}(U)$ denote the Bergman spaces on $\Omega $ and $U$, respectively.

Citation

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Sönmez Şahutoğlu. "Localization of compactness of Hankel operators on pseudoconvex domains." Illinois J. Math. 56 (3) 795 - 804, Fall 2012. https://doi.org/10.1215/ijm/1391178548

Information

Published: Fall 2012
First available in Project Euclid: 31 January 2014

zbMATH: 1296.32014
MathSciNet: MR3161351
Digital Object Identifier: 10.1215/ijm/1391178548

Subjects:
Primary: 32W05 , 47B35

Rights: Copyright © 2012 University of Illinois at Urbana-Champaign

Vol.56 • No. 3 • Fall 2012
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