关于C^n中具有逐块光滑边界的有界域上C-L公式与C-F公式的拓广式

EXTENDED FORMS OF C-L FORMULA AND C-F FORMULA ON BOUNDED DOMAIN WITH PIECEWISE SMOOTH BOUNDARY IN C^n

得到了Ｃｎ空间中具有逐块Ｃ（１）光滑边界的有界域上光滑函数的一个抽象的积分公式．这个公式的特点是积分核中含有一系列向量函数Ｗ（０，Ｋ）（，ｚ），Ｗ（ｉ，ｋ）（，ｚ）及一系列独立的实参数由这个公式，适当选取其中的参数和向量函数Ｗ，就可得到具有这种逐块Ｃ（１）光滑边界的有界域上光滑函数的Ｃａｕｃｈｙ－Ｌｅｒａｙ公式和全纯函数的Ｃａｕｃｈｙ－Ｆａｎｔａｐｐｉｅ公式以及其它一些新的公式．

An abstract integral formula of smooth functions on bounded domain with piecewise smooth boundary in Cn is obtained, the characteristic property of which is that the integral kernel contains a series of vector functions W(0,k)(s, z), W(i,k)(, z) and a series of independent real parameters μok≥ 0, μik ≥0. mom this formula, when the proper parameter aid and vector function W are chosen, we can obtain Cauchy-Leray formula of smooth functions, Cauchy-Fantappie formula of holomorphic functions and some other new formulas on bounded domain with piecewise C(1) smooth boundary.