闭逐块光滑流形上的Cauchy－Fantappie型积分的边界性质

对Ｃ￣ｎ空间中具有逐块Ｃ￣（１）光滑可定向边界Ｄ的有界域Ｄ和著名的Ｃａｕｃｈｙ－Ｆａｎｔａｐｐｉｅ公式，本文定义一类与Ｂｏｃｈｎｅｒ－Ｍａｒｔｉｎｅｌｌｉ核同伦等价的Ｃ－Ｆ核Ω，应用同伦方法证明具有Ｈｏｌｄｅｒ密度的相应奇异积分Ｆ（ｔ）存在哥西主值和Ｃ－Ｆ型积分Ｆ（ｚ）存在满足Ｈｏｌｄｅｒ条件的内、外极限值Ｆ￣＋（ｔ）和Ｆ￣－（ｔ）；同时建立一个更一般的含有边界上点ｔ的立体角系数α（ｔ）的Ｐｌｅｍｅｌｊ公式。

Boundary Behaviour for the Integrals of Cauchy-Fantappie Type on a Closed Piece- wise Smooth Manifold

For the bounded domain D in the space C￣n with orientable piecewise smooth bound-ary D of class C￣(1),and the well known Cauchy-Fantappie integral formula, the author definesakind of Cauchy-Fantappie kernel Ω which is homotopy equivalent to Bochner-Martinelli kernel.and uses homotopy method to prove that the singular integraI F(t) with kernel Ω and Holdercontinuity density f (t) possess Cauchy principal value and the C-F type integral F(z) possessinner and outer limit value F￣+(t)and F(t)satisfying the Holder condition; and the authorest ablishes a more general Plemelj formula which involves a solid angle coefficient α(t)at thepoint t ∈D。