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

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.