| Clifford分析中k-正则函数的一些性质和高阶Cauchy型积分的边值特性 |
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| 引用本文： | 李小伶,乔玉英,扈玮玮,王海燕.Clifford分析中k-正则函数的一些性质和高阶Cauchy型积分的边值特性[J].数学进展,2010(1). |
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| 作者姓名： | 李小伶 乔玉英 扈玮玮 王海燕 |
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| 作者单位： | 河北师范大学数学与信息科学学院; |
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| 基金项目： | 国家自然科学基金资助项目(No.10771049,No.10671207); 河北省自然科学基金资助项目(No.A2007000225). |
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| 摘 要： | 本文首先给出了定义于R~n取值于Clifford代数C(V_(n,0))中k-正则函数的若干性质,如唯一性定理,Cauchy-Pompeiu公式,高阶Cauchy积分公式,平均值定理等,然后在k-正则函数的高阶Cauchy积分公式的基础上,相应的定义了r次连续可微函数的高阶Cauchy型积分,并给出了它的Cauchy主值,Plemelj公式,边值的Ho|¨lder连续性及其Privalov定理.
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| 关 键 词： | 唯一性定理 平均值定理 高阶Cauchy型积分 Plemelj公式 Privalov定理 |
Some Properties of the k-regular Functions and Boundary Behavior of the Higher Order Cauchy-type Integral in Clifford Analysis |
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| LI Xiaoling,QIAO Yuying,HU Weiwei,WANG Haiyan.Some Properties of the k-regular Functions and Boundary Behavior of the Higher Order Cauchy-type Integral in Clifford Analysis[J].Advances in Mathematics,2010(1). |
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| Authors: | LI Xiaoling QIAO Yuying HU Weiwei WANG Haiyan |
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| Institution: | LI Xiaoling,QIAO Yuying,HU Weiwei,WANG Haiyan (College of Mathematics , Information Science,Hebei Normal University,Shijiazhuang,Hebei,050016,P.R.China) |
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| Abstract: | In this paper,firstly,some properties of the k-regular functions defined in R~n and with values in Clifford algebra C(V_(n,0)) are proved,such as unique theorem,Cauchy-Pompeiu formular,higher order Cauchy integral formular,mean value theorem and so on.Secondly,on the base of the higher order Cauchy integral for k-regular functions,the higher order Cauchy-type integral for the r times continuously differential functions is correspondingly introduced,and its Cauchy principal value,Plemelj formula and the boun... |
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| Keywords: | unique theorem mean value theorem higher order Cauchy-type integral Plemelj formula Privalov theorem problem |
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