In this paper we systematically study the Riemann boundary value problems on the hyperplane for monogenic functions in Clifford analysis. The concept of the principal part of a sectionally regular function with the hyperplane as its jump surface is first introduced. Based on this concept the general forms of the Riemann boundary value problems on the hyperplane for monogenic functions are formulated. Then, the explicit expressions and explicit solvable conditions for solutions with any finite integer order at infinity are obtained.

中文翻译：

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超平面上单基因函数的黎曼边值问题

本文系统地研究了Clifford分析中单基因函数超平面上的黎曼边值问题。首先介绍了以超平面为跳面的截面正则函数的主体部分的概念。基于这个概念，制定了单基因函数超平面上黎曼边值问题的一般形式。然后，得到了无穷处任意有限整数阶解的显式表达式和显式可解条件。