The Properties Of Integral Operator With K-regular Kernel In Clifford Analysis

The properties of the T(Teodorescu)operator with k-regular kernel in Clifford analysis are defined and studied in this paper.T-operator is a singular integral operator defined in domain.In complex analysis and Clifford analysis,many results about T-operator are well developed.However,the properties of the T-operator with k-regular kernel in Clifford analysis haven't been studied.The k-regular function is natural generalization of the regular function in Clifford analysis.It is the element in null space of operator Dk which is based on the Dirac operator D =(?).The T-operator plays an important role in application of mathematics,especially in the expression of the solution of the equation,so it is necessary to study the properties of the T-operator with k-regular kernel in Clifford analysis.This paper defines the T-operator with k-regular kernel in Clifford analysis and focusses on the basic properties of it.We obtain uniform boundedness,H(?)lder continuity and ? times integrability of the T-operator with k-regular kernel in bounded domain.Based on this,some results of this paper are obtained in Lp,n(Rn)space.This paper consists of three chapters.Chapter 1 introduces the fundamental structure and arithmetic rule of Clifford al-gebra,and gives the preliminary knowledge and some related lemmas.Chapter 2 firstly provides a definition of the T-operator with k-regular kernel in Clif-ford analysis,and then provides the properties,including uniform boundedness,H(?)lder continuity and ? times integrability,of this operator in bounded domain.Chapter 3 discusses the properties of the operator in Lp,n(Rn)space,including uni-form boundedness and H(?)lder continuity.