Clifford分析中高维空间上两类高阶T算子的性质.pdfVIP

Abstract The basic properties of two types of high-order T(Teodorescu)-operators are studied in Clifford analysis in this paper. T-operator is a singular integral operator defined in the region. As we know, T-operator plays a very important role in the generalized analytic functions and Vekua system. And Vekua system closely related to the plane elasticity, shell theory, aerodynamics and so on.Then it’s necessary to study the properties of T-operators in various spaces.While T- operator is the generalized solution of the non-homogeneous Dirac equation. Therefore it plays a key role when we study the integral expression of non-homogeneous Dirac equation and many boundary value problems. In Complex analysis,many theories about T-operator are well development. But in Clifford analysis, T-operator, especially the natures of high-order singular T-operator ,has no correspond- ing conclusions. The T-operator in high-dimensional space in Clifford analysis is the promotion of T-operator in complex plane. It has many of the same natures of the T-operator in complex plane. Meanwhile,the high-order singular T-operator in Clifford analysis also has many good properties and applications. The paper focuses on the basic natures of a generalized Teodorescu operator which has high-order singular in Clifford analysis .We obtain uniform boundedness, ¨ Holder continuity of the operator in R space . At the same time we also prove the γ times inte- grability of the operator. In addition, many basic properties of a high-order singular T-operator defined in L (Ω) space are studied in this paper.And we obtain the uniform boundedness, ¨ Holder continuity of the operator in R space.We also get the nature of the operator at infinity. This paper is divided into three chapters. In chapter 1, we give the prior knowle