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Clifford分析中Isotonic柯西型积分的边界性质
  • 期刊名称：数学学报中文版
  • 时间：0
  • 页码：177-186
  • 语言：中文
  • 分类：O177.4[理学—数学;理学—基础数学]
  • 作者机构：[1]淆华大学计算机科学与技术系,北京100084, [2]武汉大学数学与统计学院,武汉430072, [3]清华大学计算机科学与技术系,北京10084
  • 相关基金：国家863项目（2009AA011906）; 国家自然科学基金资助项目（10871150 60873249）; 博士后基金（20090460316 201003111）
  • 相关项目：复与超复分析中边值问题与奇异积分方程
作者： 库敏，杜金元，王道顺|
关键词： CLIFFORD分析, Isotonic柯西型积分, Privalov定理, Clifford analysis, Isotonic Cauchy type integral, Privalov theorem
中文摘要：

本文主要刻画了定义于偶数维欧氏空间中光滑曲面而取值于复Clifford代数的isotonic柯西型积分的边界性质.对具有H（o｜¨）lder密度函数的isotonic柯西型积分,得到了Privalov定理和Sokhotskii-Plemelj公式,并证明了多复变函数论中经典Bochner-Martinelli型积分的Privalov定理和Sokhotskii-Plemelj公式为其特殊情形.

英文摘要：

The holomorphic functions of several complex variables are closely related to the so-called isotonic Dirac system in which different Dirac operators in the half dimension act from the left and from the right on the functions considered.In this paper we mainly study the boundary properties of the isotonic Cauchy type integral operator over the smooth surface in Euclidean space of even dimension with values in a complex Clifford algebra.We obtain Privarlov tneorem inducing Sokhotskii-Plemelj formula as the special case for the isotonic Cauchy type integral operator with H（o｜¨）lder density functions taking values in a complex Clifford algebra,and show that Privalov theorem of the classical Bochner-Martinelli type integral and the classical Sokhotskii-Plemelj formula over the smooth surface of Euclidean space for holomorphic functions of several complex variables may be derived from it.

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