Steadiness Of Bochner-Martinelli Integrals Wit Perturbation On The Boundary On Strictly Pseudoconvex Domain

In this article,a perturbation factor r was introduced into the integral boundary of the Bochner-Martinelli Integrals on strictly pesudoconvex domain .When the norm of r is small enough,the B-M Integrals are steady and controllable . And the influence of r to B-M Formula was also argued.In Chapter One, there is some preparing knowledge.It mainly introduced some definitions and lemmas.such as strictly plurisubharmonic functions,strictly pseudoconvex domain,the orientation of complex manifolds,the norm for strictly plurisubharmonic C²- functions,and so on.The main results are in Chapter Two.The Bochner-Martinelli Integrals (?) is introduced in the first part.A per-turbating factor r is introduced to the integral boundary of the B-M Integrals (The r here is a strictly plurisubharmonic function).The perturbated boundary is (?)D_r (z^* = z + r(z)∈(?)D_r,z∈(?)D).So we get the B-M Integrals with perturbated integral boundary (?)The B-M Formula of holomorphic functions is introduced in Part Two.And the influence of the perturbating factor r to the B-M Formula is also argued .And we get the result that after perturbation to the integral boundary of the B-M Formula,the B-M Formula is relatively steady and it has got its beauty in form.We also get some related results.A holomorphic function being perturbated by r remains to be holomorphic.A strictly pesudoconvex domain with piece-wise C²- smooth boundary ,being perturbated by r ,is still with a piece- wise C²- smooth boundary. But a strictly plurisubharmonic function being perturbated by r may not remain its original charactors.In Part Three,the steady of the B-M Formula with perturbation to the integral boundary is studied. In Part Two,the B-M Formula of holomorphic functions concerned with holomorphic fuctions satisfied with Holder conditions.The cauchy Principle Value is used to argue the steadiness of the B-M Integrals. Then we get the result that the B-M Integrals with perturbation to the boundary are steady and controllable.In Part Four,the operators B_(?)D, B_d and the B-M Formula of continuous functions are introduced ,and the influence of boundary perturbation to the B-M Formula is also studied.And we also get the relatively steady result and formal beauty.When the continuous functions are ristricted to be holomorphic, we find out the result admits very well with that in Part Two ,Chapter Two.