Painleve定理的拓广

The Extension of Painleve Theorems

R2中的Painleve定理在求解方程的边值问题中有十分重要的作用。此定理对多复变数中的Cauchy型积分的边界行为的研究也起关键作用。将R2中的Painleve定理推广到Cn(n>1)中,得到复的Painleve定理。并简述其在多复变数奇异积分研究中的应用。

Painleve Theorems in R^2 have significant effect in the research of the boundary problem. These theorems are also the key in the study of boundary behavior of Cauchy type integral in C^n （n〉1）. The author extend Painleve Theorems in R^2 to C^n （n 〉 1 ）, and obtain the complex version Painleve Theorems. As an application, the author briefly expound how Painleve Theorems can be applied in the study of singular integral in several complex variables.