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  

Some Properties of the k-regular Functions and Boundary Behavior of the Higher Order Cauchy-type Integral in Clifford Analysis

作　　者：李小伶[1] 乔玉英[1] 扈玮玮[1] 王海燕[1] 

机构地区：[1]河北师范大学数学与信息科学学院,石家庄河北050016

出　　处：《数学进展》2010年第1期31-48,共18页Advances in Mathematics（China）

基　　金：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).

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.In this paper, firstly, some properties of the k-regular functions defined in R^n and with values in Clifford algebra C（Vn,o） 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 boundary value HSlder continuity, the Privalov theorem are discussed explicitly.

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 

分 类 号：O177.4[理学—数学]