Clifford分析中具有超正则核的T算子的性质  

The Properties of T-operator with Hypermonogenic kernel in Clifford Analysis

作　　者：马韶瑜[1] 乔玉英[1] 杨贺菊[2] 

机构地区：[1]河北师范大学数学与信息科学学院,河北石家庄050024 [2]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》2014年第1期256-263,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11301136);河北省自然科学基金(A2010000346)

摘　　要：讨论了Clifford分析中具有超正则核的T(Ieodorescu)算子的基本性质.T算子是定义在区域上的奇异积分算子,它在广义解析函数理论和Vekua理论中起着重要的作用.在复分析中关于T算子的理论已经发展得很完善,但在Clifford分析中,具有超正则核的T算子的相关性质还没有得到研究.研究了Clifford分析中具有超正则核的T算子的基本性质,得到了这个算子在ΩR_+^(n+1)上的一致有界性,Hlder连续性以及这个算子的γ次可积性.The basic properties of the T（Teodorescu） operator with hypermonogenic kernel in Clifford analysis are studied in this paper. T-operator is a singular integral operator defined in a domain and it plays an important role in generalized analytic function and Vekua theory. In Complex analysis, many theories about T-operator are well development. But in Clifford analysis, it hasn＇t been studied about the properties of a T-operator with hypermonogenic kernel. The paper focuses on the basic properties of T-operator which has hypermonogenic kernel in Clifford analysis. We obtain its uniform boundedness and HSlder continuity in Ω Rn＋1 ＋ space. At the same time we also prove the γtimes integrability of the operator.

关 键 词：超正则函数 Teodorescu算子 一致有界性 HOLDER连续性 γ次可积性 

分 类 号：O177[理学—数学]