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

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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n+1}}$$\end{document} with Hölder-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 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{R}^{n+1}}$$\end{document} . As special cases solutions of the corresponding boundary value problems for the classical poly-analytic and meta-analytic functions are also derived, respectively.