The Properties Of Quasi-Cauchy Type Integral Of Hypermonogenic Functions In Clifford Analysis

In this paper, we study the hypermonogenic functions which are the solutions of Dirac-Hodege equation in upper half space endowed with the hyperbolic metric. The Cauchy formula of hypermonogenic functions is represented by the quasi-Cauchy type integral. Firstly we show some basic properties of quasi-Cauchy type integral. Secondly we obtain Plemelj formula of hypermonogenic functions in Clifford analysis. Finally we prove the representation theorem of a C~1 function which is called Borel-Pompeiu formula.