闭光滑流形上一类带拓广的B-M核的高阶奇异积分方程

One Higher Order Singular Integral Equations with Extensional B-M Kernel on Smooth Closed Orientable Manifolds

根据文献[1]在Cn中闭光滑可定向流形上定义的一个带有拓广的B-M核的高阶Cauchy型积分φ(z)以及φ(z)在Hadamard主值[2]意义下的Plemelj公式[2],在Hadamard主值意义下给出高阶奇异积分φ(t)的有限部分的合成公式;然后通过合成公式讨论了相应的一类高阶奇异积分方程。

According to the article[1] where the authors defined one higher order integral of Cauchy-type with extensional Bochner-Martinelli kernelφ（z） on smooth closed orientable manifolds in Cn and the plemelj formula of φ（z） under the definition of Hadamard principal value.The author will give the composite formula of the finite part of the higher order singular integral φ（t） under the definition of Hadamard principal value in this article.At last,the authors will discuss one higher order singular integral equations by using the composite formula.