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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

Received by editor(s): November 1, 2001
Published electronically: July 26, 2002
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2002 American Mathematical Society