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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A local geometric characterization of the Bochner-Martinelli kernel


Author: Michael Bolt
Journal: Proc. Amer. Math. Soc. 131 (2003), 1131-1136
MSC (2000): Primary 32A26; Secondary 53A07
Published electronically: July 26, 2002
MathSciNet review: 1948104
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Abstract: In this paper it is shown that a connected smooth local hypersurface in $\mathbb C^{n}$ for which the skew-hermitian part of the Bochner-Martinelli kernel has a weak singularity must lie on a surface having one of the following forms: $S^{2m+1} \times \mathbb C^{n-m-1}$ for some $1\leq m <n$, or $C\times \mathbb C^{n-1}$ where $C$ is a one-dimensional curve. This strengthens results of Boas about the Bochner-Martinelli kernel and it generalizes a result of Kerzman and Stein about the Cauchy kernel.


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Additional Information

Michael Bolt
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: mbolt@umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06699-6
PII: S 0002-9939(02)06699-6
Received by editor(s): November 1, 2001
Published electronically: July 26, 2002
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2002 American Mathematical Society