Stein流形上(p,q)型微分形式的Koppelman-Leray公式的拓广

The Generalization of Koppelman-Leray Formula of Differential Form of( p,q)-type on Stein Manifold

为进一步研究 Stein流形上的 Koppelman- Leray公式 ,采用 Bochner- Martinelli的方法 ,并将之推广到 Stein流形上 .便可得到一个 Stein流形上 (p,q)型微分形式的 Koppelman- Leray公式的一种拓广式 ,该拓广式的特点是积分核中含有可供选择的实参数 m及 (D,s,φ)的 Leray截面 ,当 m=2时 ,可得到 Stein流形上已有的 (p,q)型微分形式的 Koppelman- Leray公式 ,而当取 m=3,4,… ,N(N<+∞ )时 ,可相应得到 Stein流形上一系列积分核彼此不同的积分公式 .由该拓广式还可得到 Cn空间中 (p,q)型微分形式 Koppelman- Leray公式在

In order to futher the study of the Koppelman- Leray formula of differential form of( p,q) - type on Stein manifold,the method of Bochner- Martinelli is adopted and extended to Stein manifold.The generalization of Koppelman- Leray Formula of Differential form of ( p,q) - type on Stein manifold is obtained.The property of this formula is that the integral kernel contains a L eray section of( D,s,φ) and a real parameter m which can be chosen. When m is epual to2 ,the know Koppelman- Leray formula of differential form of( p,q) - type on Stein manifold is obtained,and when m is 3,4,… ,N ( N <+∞ ) ,a series of different integral formulas with different integral kernels on stein manifold can be obtained accordingly.The relevant generalization on Stein manifold of Koppelman- L eray formula of differential form of( p,q) - type in Cn can also be obtained.