A kind of Riemann boundary value problems for pseudo-harmonic functions in Clifford analysis

Abstract

In this article, some properties of singular integrals with parameter are discussed. We prove a Liouville-type theorem for pseudo-monogenic functions and pseudo-harmonic functions. With the help of them, R −1 Riemann boundary value problems for pseudo-monogenic functions and pseudo-harmonic functions with values in a Clifford algebra Cl(V 3.3) are investigated in the classical sense and their explicit representation of solutions are obtained.