The property of Teodorescu operator with higher singularity in Clifford analysis

Abstract

In this paper, we define a kind of singular Teodorescu operator with order n+α+1 in Lp 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.