数学学报 2011, 54(2) 177-186 DOI:      ISSN: 0583-1431 CN: 11-2038/O1

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本文关键词相关文章
Clifford分析
Isotonic柯西型积分
Privalov定理
Plemelj公式
本文作者相关文章
库敏
杜金元
王道顺
Clifford分析中Isotonic柯西型积分的边界性质
库敏1, 杜金元2, 王道顺1
1. 清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
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Hölder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.

 

关键词 Clifford分析   Isotonic柯西型积分   Privalov定理   Plemelj公式  
MSC2000 O177.4
The Boundary Behavior of Isotonic Cauchy Type Integral in Clifford Analysis
Min KU1, Jin Yuan DU2, Dao Shun WANG1
1. Department of Computer Science and Technology, Tsinghua University, Beijing 100084, P. R. China;
2. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, P. R. China
Abstract:
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 Privalov theorem inducing Sokhotskii-Plemelj formula as the special case for the isotonic Cauchy type integral operator with Hölder 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.

 

Keywords: Clifford analysis   Isotonic Cauchy type integral   Privalov theorem  
收稿日期 2009-07-08 修回日期 2010-09-30 网络版发布日期  
DOI:
基金项目:

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)

通讯作者:
作者简介:
作者Email: kumin0844@163.com; jydu@whu.edu.cn; daoshun@mail.tsinghua.edu.cn

参考文献:


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