Some Properties Of Infrapolymonogenic Functions And Related Boundary Value Problems

Firstly,this paper studies some properties of infrapolymonogenic functions,including uniqueness theorem,a judgment theorem of infrapolymonogenic functions and mean value theorem.Secondly,the continuity of the integral operator C?ifp,k[f]related to infrapolymonogenic functions and the Plemelj formula of infrapolymonogenic functions are proved.Finally,the integral representation of the solution of Riemann boundary value problem related to infrapolymonogenic functions is given by using the above conclusions.The details are as follows:In Chapter 1,some preliminary knowledge are given,mainly introduces Clifford algebra,infrapolymonogenic functions and related operators and lemmas.In Chapter 2,it is proved that the uniqueness theorem,a judgment theorem of infrapolymonogenic functions and mean value theorem,which make us have a further understanding of infrapolymonogenic functions.In Chapter 3,firstly,some related definitions and lemmas are given.Secondly,it is proved that the integral operator C?ifp,k[f]related to the infrapolymonogenic functions is Holder continuous on ?,and Holder continuous within ?+(?-).When a point is on the boundary ?,another point inside ?+(?-),it is aslo Holder continuous.Thus,the continuity of integral operator C?ifp,k[f]on Rn is proved.Finally,the Plemelj formula of infrapolymonogenic functions is given.In Chapter 4,firstly,some related lemmas are given.Secondly,it is proved that(C?ifp,k[f])(x)satisfies ?x2k-1(C?ifp,k[f])(x)?x=0,that is,(C?ifp,k[f])(x)is a infrapolymonogenic function.Finally,the integral representation of Riemann boundary value problem related to infrapolymonogenic functions is given by the above conclusions.