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Compactness of Hankel Operators with Symbols Continuous on the Closure of Pseudoconvex Domains

  • Timothy G. Clos
  • Mehmet Çelik
  • Sönmez Şahutoğlu
Article

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 \(f:{\mathbb {D}}\rightarrow b\Omega \).

Keywords

Hankel operators Convex domains Pseudoconvex domains 

Mathematics Subject Classification

Primary 47B35 Secondary 32W05 

Notes

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.

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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsBowling Green State UniversityBowling GreenUSA
  2. 2.Department of Mathematics and StatisticsUniversity of ToledoToledoUSA
  3. 3.Department of MathematicsTexas A&M University - CommerceCommerceUSA

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