A local geometric characterization of the Bochner-Martinelli kernel
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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.References
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Additional Information
- Michael Bolt
- Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
- Email: mbolt@umich.edu
- Received by editor(s): November 1, 2001
- Published electronically: July 26, 2002
- Communicated by: Mei-Chi Shaw
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 1131-1136
- MSC (2000): Primary 32A26; Secondary 53A07
- DOI: https://doi.org/10.1090/S0002-9939-02-06699-6
- MathSciNet review: 1948104