C~n中具非光滑边界的强拟凸多面体上的一个积分表示
An Integral Representation Formula for Strictly Pseudoconvex Polyhedrons with Non-smooth Boundaries in C~n
Abstract
得到Cn 中具逐块C( 1) 边界的强拟凸多面体上含参数的Koppelman Leray Norguet公式及Cn 中边界不必光滑的强拟凸多面体上含参数的Koppelman Leray Norguet公式 ,并相应得到 方程的解 ,其特点是含有可供选择的实参数m =2 ,3,… ,N(N <+∞ )且不含边界积分 ,从而避免了边界积分的复杂估计 A generalization of Koppelman-Leray-Norguet formula for strictly pseudoconvex polyhedrons with piecewise C (1)smooth boundaries and for strictly pseudoconvex polyhedrons with non-smooth boundaries in C n is obtained,and the solutions of the corresponding -equations which contain the parameter m, m=2,...,N(N<+∞) and don't involve integral on boundary are given, thus avoiding the complexity estimations of the boundary integral.