C^n空间中具有逐块光滑边界的有界域上K-L-N公式的拓广式

The Extensional K-L-N Formula on a Bounded Domain with Piecewise Smooth Boundaries in C^n

应用单位分解的观念及核函数的构造理论,首先在Cn空间中具有逐块光滑边界的有界域上引进一种抽象的单位分解并构造一个核函数,然后在拓广的Koppelman公式的基础上,应用Stokes公式,得到Cn空间中具有逐块光滑边界的有界域上连续有界(0,q)型微分形式的一种抽象的积分表示式和-方程的连续解.由这个抽象的积分表示式,当适当选择其中的向量函数和参数时,可得到现有的其它许多积分公式和它们的拓广式.

By means of the conception of partition of unity and the structure theory of kernel function,an abstract partition of unity is introduced and a kernel function is constructed on a bounded domain with piecewise smooth boundaries in C^n. Then, using the extensional Koppelman formula and Stokes formula, the author obtained an abstract integral representation formula of （O,q）-form and the continuous solution of δ^- equation on a bounded domain with pieeewise smooth boundaries in C^n. From this abstract integral formula,we can obtain many other integral formulas and extensional formulas, when the vector functions and parameters are suitahlly chosen.