强拟凸域上边界摄动的B-M型积分的稳定性

Stability of Bochner-Martinelli Integrals with Perturbation on the Boundary on Strictly Pseudoconvex Domain

为了考察强拟凸域上的B-M型积分,当积分边界发生摄动时,是否仍然稳定,在B-M型积分Φ(φ)(z)=ζ∫∈Dφ(ζ)K(ζ,z),z∈D的积分边界引入一个摄动因子r,得到边界摄动的B-M型积分Φr(φ)(z)=ζ∫*∈Drφ(ζ*)K(ζ*,z)=t∫∈Dφ(t+r(t))K(t+r(t),z).讨论了摄动函数r对全纯函数的B-M公式的影响,得到全纯函数的B-M公式的积分边界受到摄动以后,B-M公式是相对稳定的,并具有形式上的美.同时也得到相关的结论,全纯函数经r摄动以后仍为全纯函数;但强多次调和函数经r摄动以后,未必保持原有性质.并用Cauchy主值讨论B-M型积分的稳定性,得到边界摄动的B-M型积分是稳定的,可控制的.

In order to study whether the B-M Integrals on strictly pesudoconvex domain were still of stability or not,when perturbated,a perturbation factor r was introduced into the integral boundary of B-M Integral φ（φ）（z）=∫ζ^＊∈δD.Then a boundary perturbated B-M Integral was produced.φ（φ）（z）=∫ζ^＊∈δD.φ（t＋r（t））K（t＋r（t）,z）. After being perturbated on the integral boundary of B-M Formula, B-M Formula is relatively steady and has a formal beauty. At the same time,a perturbated holomorphic function is still holomorphic; but a perturbated strictly plurisubharmonic function may not remain strictly plurisubharmonie. Cauchy Principal Value was introduced to argue the stability of B-M Integrals. As a result,a boundary perturbated B-M Integral is steady and controllable.