数学物理学报(英文版)

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PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS

  

  1. Department of Mathematics, Xiamen University, Xiamen 361005, China
  • 出版日期:2005-10-11 发布日期:2005-10-11
  • 基金资助:

    The project was supported by the Natural Science
    Foundation of Fujian Province of China (Z0511002) and the National Science Foundation of China (10271097)
    Chen L P, the corresponding author.

PLEMELJ FORMULA OF CAUCHY TYPE INTEGRAL ON STEIN MANIFOLDS

  • Online:2005-10-11 Published:2005-10-11
  • Supported by:

    The project was supported by the Natural Science
    Foundation of Fujian Province of China (Z0511002) and the National Science Foundation of China (10271097)
    Chen L P, the corresponding author.

摘要:

Let D be a bounded domain with piecewise C(1) smooth orientable boundary
on Stein manifolds, and let (z) be a Cauchy type integral with Bochner-Martinelli kernel

(' , ¯ S, S) and H¨older continuous density function '(), the authors define a solid angular
coefficient (t) at the point t 2 @D, prove that there exist the interior and outer limit values
±(t) under the meaning of the Cauchy principal value, and obtain the more general
Plemelj formula and jump formula.

Abstract:

Let D be a bounded domain with piecewise C(1) smooth orientable boundary
on Stein manifolds, and let (z) be a Cauchy type integral with Bochner-Martinelli kernel

(' , ¯ S, S) and H¨older continuous density function '(), the authors define a solid angular
coefficient (t) at the point t 2 @D, prove that there exist the interior and outer limit values
±(t) under the meaning of the Cauchy principal value, and obtain the more general
Plemelj formula and jump formula.

Key words: Stein manifold, Cauchy type integral, Plemelj formula, solid angular coeffi-cient

中图分类号: 

  • 32A25