The property of Teodorescu operator with higher singularity in Clifford analysis

In this paper, we define a kind of singular Teodorescu operator with order n+α+1 in L_p space with valued in Clifford algebra. We discuss its boundedness and Hölder continuity. And the works lay a strong foundation for the studies of boundary value problems of degenerate equations in Clifford analysis. Moreover boundary value problems of various equations and extreme value problem of it´s solution have been widely apply in theory of control, signal processing and so on.