中文摘要：

C″（n〉1）中的广义上半空间是一特殊的无界域．本文利用广义上半空间上的全纯的Cauchy-Fantappie核研究了Cauehy型积分的边界行为，得到了奇异积分的Cauchy主值的存在性．此处Cauchy型积分的密度函数是一类特殊的Holder函数．进一步研究了Cauehy型积分的边界极限值，得到了Plemelj公式．广义上半空间中Cauchy型积分在无穷远点处的边界行为的处理是无界域情形特有的．

英文摘要：

The generalized upper half space in C＂ （n〉1） is an unbounded domain. In this paper by using the holomorphic Cauchy- Fantappi~ kernel of the generalized upper half space the boundary behavior of the Cauchy type integral on the generalized upper half space is studied, and the existence of the principal value of the singular integral is obtained. The density functions in the Cauchy type integral are a kind of special Hoder functions. The boundary limit value of the Cauchy type integral is further studied, and Plemelj formula is obtained. The operation on the boundary behavior at the infinity point in the Cauchy type integral on the generalized upper half space is peculiar to the case of the unbounded domain.