泛Clifford分析中具有双LR正则核的奇异积分算子的性质  

Properties of Singular Integral Operators with Double LR Regular Kernel in Universal Clifford Analysis

作　　者：李万营 郭欣 杨贺菊[1] LI Wan-ying;GUO Xin;YANG He-jui(College of Science,Hebei University of Science and Technology,Shijiazhuang 050018,China)

机构地区：[1]河北科技大学理学院,河北石家庄050018

出　　处：《数学的实践与认识》2024年第3期213-223,共11页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11871191);河北省自然科学基金(A2022208007)。

摘　　要：泛Clifford分析是Clifford分析更为一般化的推广.首先研究泛Clifford代数上双LR正则函数的Cauchy积分表示,以及其Cauchy型主值积分的性质.通过定义L正则函数,R正则函数,LR正则函数,双LR正则函数给出泛Clifford分析中双LR正则的核函数,并给出其Cauchy积分表示.最后通过插项的方法研究了一类泛Clifford分析中具有双正则核的Cauchy型奇异积分算子的收敛性.The universal Clifford analysis is a more general generalization of the Clifford analysis.In this paper,we first study the Cauchy integral representation of double LR regular functions on a universal Clifford algebra and the properties of Cauchy type principal valued integrals.By defining LRegular function,R regular function,LR regular function,double LR regular function The kernel function of double LR regular in universal Clifford analysis is given,and its Cauchy integral representation is given.Finally,the convergence of Cauchy type singular integral operators with biregular kernel in universal Clifford analysis is studied by means of interpolation.

关 键 词：泛Clifford代数 双LR正则函数 奇异积分算子 Cauchy主值积分 

分 类 号：O177.6[理学—数学]