Some Integral Representations and Singular Integral over Plane in Clifford Analysis

In this paper, Cauchy type integral and singular integral over hyper-complex plane are considered. By using a special Mobius transform, an equivalent relation between class functions over and class functions over the unit sphere is shown. For class functions over , we prove the existence of Cauchy type integral and singular integral over . Cauchy integral formulas as well as Poisson integral formulas for monogenic functions in upper-half and lower-half space are given respectively. By using Mobius transform again, the relation between the Cauchy type integrals and the singular integrals over and unit sphere is built.