一类带拓广的Bochner-Martinelli核的高阶奇异积分的Hadamard主值

The Hadamard Principal Value of One Higher Order Singular Integral with Extensional Bochner-Martinelli Kernel

首先定义Cn中闭光滑可定向流形上一个带有拓广的Bochner-Martinelli核的高阶Cauchy型积分(z),然后利用分部积分和Stokes公式,给出这个奇性为2n阶的高阶奇异积分(t)的Hadamard主值,接着通过球面坐标变换等方法证明了一些引理,由此获得了(z)在Hadamard主值意义下的Plemelj公式。

Firstly the authors define one higher order integral of Cauchy - type with extensional Bochner - Martinelli kernel Ф（z） on smooth closed orientable manifolds in C^n. Then using integration by parts and stokes formula, the authors give the definition of Hadamard principal value of the higher order singular integral th （t） whose singularities are of orders 2n . Then the authors prove some lemmas by means of the spherical coordinates etc. and obtain the plemelj formula of Ф （z） under the definition of Hadamard principal value.