The H(o|¨)lder Continuity Of Two Times Quasi-cauchy Integral In Clifford Analysis

W. k. Clifford combined space structure in high dimension and the geometric algebratheory, and then created a kind of geometric algebra named Clifford algebra. It is an non-commutable and associative algebra. Clifford Analysis is the classical functional theoryon the Clifford algebra. It is the high-dimensional generalization of the real analysis, com-plex analysis, quaternionic analysis etc. As an active branch of the mathematical study,it has significant theoretical and applicable value in mathematics and other subjects.Bihypermonogenic function s extended by monogenic function and biregular func-tion. Although they are similar in many areas, their properties and integral formulas aredifferent obviously. On the basis of Cauchy Integral formula and Plemelj formula of bi-hypermonogenic function, we study H(o|¨)lder continuity of two times quasi-Cauchy integraloperator, all of these content lay a foundation for properties and iterative approximationof bihypermonogenic function, besides, this article enrich the theory of bihypermonogenicfunction.This paper is made up of three parts: In chapter1, the preliminaries and some mainlemmas and definition of bihypermonogenic function are given. Then, in the second part,we get the two times quasi-Cauchy integral formula operator and Plemelj formula for thebihypermonogenic function. At the end, we discuss H(o|¨)lder continunity of tne two timesquasi-Cauchy integral operator for bihypermonogenic function by using of related Ho¨ldercontinunity and estimation for some singular integral operators.