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Transactions of the American Mathematical Society

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The finite part of singular integrals in several complex variables

Author: Xiaoqin Wang
Journal: Trans. Amer. Math. Soc. 337 (1993), 771-793
MSC: Primary 32A25
MathSciNet review: 1120777
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Abstract: A divergent integral can sometimes be handled by assigning to it as its value the finite part in the sense of Hadamard. This is done by expanding the integral over the complement of a symmetric neighborhood of a singularity in powers of the radius, and throwing away the negative powers. In this paper the finite part of a singular integral of Cauchy type is defined, and this is then used to describe the boundary behavior of derivatives of a Cauchy-type integral. The finite part of a singular integral of Bochner-Martinelli type is studied, and an extension of the Plemelj jump formulas is shown to hold.

References [Enhancements On Off] (What's this?)

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Keywords: Singular integral, Hadamard's finite part, Bochner-Martinelli kernel
Article copyright: © Copyright 1993 American Mathematical Society