Proceedings of the American Mathematical Society

Author(s): Michael Bolt
Journal: Proc. Amer. Math. Soc. 131 (2003), 1131-1136.
MSC (2000): Primary 32A26; Secondary 53A07
Posted: July 26, 2002
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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

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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