用统一的方法处理双全纯映照子族齐次展开式的估计

The Study for Estimation of Homogeneous Expansion of Subclasses of Biholomorphic Mappings by a Unified Method

在C^n中的单位多圆柱上或复Banach空间的单位球上引入正规化全纯映照族■_g,令正规化局部双全纯映照f(x)满足(Df(x))^(-1)f(x)∈■_g(其中x=0是f(x)-x的k+1阶零点).本文得到了f的齐次展开式的估计,该结果统一和推广了以前许多相关结论,并从推论的证明中清楚地看出双全纯映照子族之间的内在联系.

We introduce a class of holomorphic mappings Mg on the unit polydisc in C^n or the unit ball in a complex Banach space.Let f（x） be a normalized locally biholomorphic mapping on B such that（Df（x））^-1 f（x）∈Mg and f（x）-x has a zero of order k＋1 at x=0.The estimation of homogeneous expansion for f（x） is obtained. Especially,we unify and generalize many known results.Moreover,in view of proofs of corollaries,the essential relations among the subclasses of biholomorphic mappings are shown.