Acta Mathematica Sinica, Chinese Series 2011, 54(2) 177-186 DOI:      ISSN: 0583-1431 CN: 11-2038/O1

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Keywords
Clifford analysis
Isotonic Cauchy type integral
Privalov theorem
Authors
Min KU
Jin Yuan DU
Dao Shun WANG

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  
MSC2000 O177.4
Received 2009-07-08 Revised 2010-09-30 Online:  
DOI:
Fund:
Corresponding Authors:
Email: kumin0844@163.com; jydu@whu.edu.cn; daoshun@mail.tsinghua.edu.cn
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