Riemann boundary value problems for some K-regular functions in clifford analysis

In this paper, we study the Rm (m > 0) Riemann boundary value problems for regular functions, harmonic functions and bi-harmonic functions with values in a universal clifford algebra C(Vn,n). By using Plemelj formula, we get the solutions of Rm (m > 0) Riemann boundary value problems for regular functions. Then transforming the Riemann boundary value problems for harmonic functions and bi-harmonic functions into the Riemann boundary value problems for regular functions, we obtain the solutions of Rm (m > 0) Riemann boundary value problems for harmonic functions and bi-harmonic functions.