多复变数一类螺型映射子族各项齐次展开式的精细估计

Refined Esitmates of All Homogeneous Expansions for a Subclasses of Spirallike Mappings in Several Complex Variables

本文主要建立了复Banach空间单位球上与C^(n)中单位多圆柱上带有具体参数表示的一类螺型映射子族各项齐次展开式的精细估计.特别地,k+1阶齐次展开式的结果是精确的.同时给出复Banach空间单位球上与C^(n)中单位多圆柱上带有参数表示的一类k折对称双全纯螺型映射子族各项齐次展开式的估计,且k+1阶齐次展开式的结果也是精确的.所得结果包含一些先前文献的许多已有结论.

In this article,the refined estimates of all homogeneous expansions for a subclass of biholomorphic spirallike mappings which have a concrete parametric representation on the unit ball in complex Banach spaces and the unit polydisk in C^(n) are mainly established.In particular,the result is sharp for the(k+1)-th homogeneous expansion.Meanwhile the estimates of all homogeneous expansions for a subclass of k-fold symmetric biholomorphic spirallike mappings which have parametric representation on the unit ball in complex Banach spaces and the unit polydisk in C^(n) are also given,and the result is sharp for the(k+1)-th homogeneous expansion as well.Our obtained results include many known results in some prior literatures.