The Hadamard Principal Value Of One Higher Order Singular Integrals With Extensional Bochner-Martinelli Kernel

Firstly, the authors define one higher order integral of Cauchy-type with extensional Bochner-Martinelli kernel φ(z) on smooth closed orientablemanifolds 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 φ(t) whose singularities are of orders 2n . Followingly, the authors prove some lemmas by means of the spherical coordinates etc. and obtain the plemelj formula of φ(z); then obtain the composite formula of the finite partof the higher order singular integral φ(t) using the plemelj formula of φ(z).At last, the authors also discuss one higher order singular integral equations and partial differential integral equations by using the composite formula.