Compactness of Hankel Operators With Continuous Symbols on Domains in C 2

Abstract

Let \(\Omega \) be a bounded pseudoconvex domain in \({\mathbb {C}}^2\) with Lipschitz boundary or a bounded convex domain in \({\mathbb {C}}^n\) and \(\phi \in C(\overline{\Omega })\) such that the Hankel operator \(H_{\phi }\) is compact on the Bergman space \(A^2(\Omega )\). Then \(\phi \circ f\) is holomorphic for any holomorphic \(f:{\mathbb {D}}\rightarrow b\Omega \).

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Acknowledgements

We would like to thank Emil Straube for reading an earlier manuscript of this paper and for providing us with valuable comments. We also thank the referee for feedback that has improved the exposition of the paper.

Author information

Author notes

1. Timothy G. Clos

   Present address: Department of Mathematics and Statistics, Bowling Green State University, Bowling Green, OH, 43403, USA

Authors and Affiliations

1. Department of Mathematics and Statistics, University of Toledo, 2801 W. Bancroft, Toledo, OH, 43606, USA

   Timothy G. Clos & Sönmez Şahutoğlu

2. Department of Mathematics, Texas A&M University - Commerce, Commerce, TX, 75428, USA

   Mehmet Çelik

Corresponding author

Correspondence to Sönmez Şahutoğlu.

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Cite this article

Clos, T.G., Çelik, M. & Şahutoğlu, S. Compactness of Hankel Operators with Symbols Continuous on the Closure of Pseudoconvex Domains. Integr. Equ. Oper. Theory 90, 71 (2018). https://doi.org/10.1007/s00020-018-2497-8

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• Received: 31 May 2018

• Revised: 31 October 2018

• Published: 16 November 2018

• DOI : https://doi.org/10.1007/s00020-018-2497-8

Keywords

• Hankel operators
• Convex domains
• Pseudoconvex domains

Mathematics Subject Classification

• Primary 47B35
• Secondary 32W05

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