On the Riemann Boundary Value Problem for Null Solutions to Iterated Generalized Cauchy–Riemann Operator in Clifford Analysis

Abstract

In this paper we consider a kind of Riemann boundary value problem (for short RBVP) for null solutions to the iterated generalized Cauchy–Riemann operator and the polynomially generalized Cauchy–Riemann operator, on the sphere of \({\mathbb{R}^{n+1}}\) with Holder-continuous boundary data. Making full use of the poly-Cauchy type integral operator in Clifford analysis, we give explicit integral expressions of solutions to this kind of boundary value problems over the sphere of \({\mathbb{R}^{n+1}}\) . As special cases solutions of the corresponding boundary value problems for the classical poly-analytic and meta-analytic functions are also derived, respectively.