中文摘要：

本文研究了取值在Clifford代数上双正则函数及调和函数在超复平面上积分表示的问题.利用构造核函数的方法,获得了双正则函数及调和函数在超复平面上的积分表示公式,这些结果推广了Clifford分析中正则函数在超复平面上的积分表示公式.

英文摘要：

In this article, we study the integral representations over hyper-complex plane Π for bi-regular functions and harmonic functions with values in a Clifford algebra. By constructing the kernel functions, we give the integral representation formulas over hyper-complex plane Π for bi-regular functions and harmonic functions with values in a Clifford algebra. These results are extensions of integral representations over hyper-complex plane Π for regular functions.