On compactness of the -Neumann problem and Hankel operators

Authors:
Mehmet Çelik and Sönmez Şahutoğlu

Journal:
Proc. Amer. Math. Soc. **140** (2012), 153-159

MSC (2010):
Primary 32W05; Secondary 47B35

DOI:
https://doi.org/10.1090/S0002-9939-2011-11350-9

Published electronically:
August 29, 2011

MathSciNet review:
2833527

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Abstract | References | Similar Articles | Additional Information

Abstract: Let , where and are two smooth bounded pseudoconvex domains in such that Assume that the -Neumann operator of is compact and the interior of the Levi-flat points in the boundary of is not empty (in the relative topology). Then we show that the Hankel operator on with symbol is compact for every but the -Neumann operator on is not compact.

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Additional Information

**Mehmet Çelik**

Affiliation:
Department of Mathematics and Information Sciences, University of North Texas at Dallas, 7300 Houston School Road, Dallas, Texas 75241

Email:
Mehmet.Celik@unt.edu

**Sönmez Şahutoğlu**

Affiliation:
Department of Mathematics & Statistics, University of Toledo, 2801 West Bancroft Street, Toledo, Ohio 43606

Email:
sonmez.sahutoglu@utoledo.edu

DOI:
https://doi.org/10.1090/S0002-9939-2011-11350-9

Keywords:
$\overline{\partial}$-Neumann problem,
Hankel operators,
non-pseudoconvex domains

Received by editor(s):
August 24, 2010

Published electronically:
August 29, 2011

Additional Notes:
The second author is supported in part by the University of Toledo’s Summer Research Awards and Fellowships Program

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2011
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.