C^n中实超平面上的奇异积分

Singular Integrals on the Real Hyperplane in C^n

C^n(n>1)中的上半空间是一个不能和任何有界区域双全纯等价的无界区域,其边界为C^n中的实超平面.在C^n中的上半空间可以在一定意义下定义具有Bochner-Martinelli核的Cauchy型积分.该文采用这种Cauchy型积分研究C^n中实超平面上Bochner-Martinelli型奇异积分,得到Cauchy主值与Plemelj公式.

The upper space in Cn is an unbounded domain which cannot be biholomorphically equivalent to any bounded domain, and its boundary is the real hyperplane in C~. The Cauchy type integral with Bochner-Martinelli kernel in the upper space in Cn can be defined in some sense. In this paper, by using this Cauchy type integral, the Bochner-Martinelli type singular integral on the real hyperplane in Cn is studied, and the Cauchy principal value and the Plemelj formula are obtained.