用统一的方法处理双全纯映照子族齐次展开式的估计

徐庆华, 刘太顺

数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1189-1198.

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数学学报 ›› 2009, Vol. 52 ›› Issue (6) : 1189-1198. DOI: 10.12386/A2009sxxb0148
论文

用统一的方法处理双全纯映照子族齐次展开式的估计

    徐庆华1, 刘太顺2
作者信息 +

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

    Qing Hua XU1, Tai Shun LIU2
Author information +
文章历史 +

摘要

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 , 令正规化局部双全纯映照f(x) 满足 (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.  

Abstract

We introduce a class of holomorphic mappings on the unit polydisc in or the unit ball in a complex Banach space. Let f(x) be a normalized locally biholomorphic mapping on B such that 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.  

关键词

齐次展开式的估计 / α 次的殆β 型螺形映照 / α 次的β 型螺形映照

Key words

The estimation of homogeneous expansion / almost spirallike mapping of type β and order α / spirallike mapping of type β and order α

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导出引用
徐庆华, 刘太顺. 用统一的方法处理双全纯映照子族齐次展开式的估计. 数学学报, 2009, 52(6): 1189-1198 https://doi.org/10.12386/A2009sxxb0148
Qing Hua XU, Tai Shun LIU. The Study for Estimation of Homogeneous Expansion of Subclasses of Biholomorphic Mappings by a Unified Method. Acta Mathematica Sinica, Chinese Series, 2009, 52(6): 1189-1198 https://doi.org/10.12386/A2009sxxb0148

参考文献



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基金

浙江省自然科学基金重大项目(D7080080);江西省自然科学基金项目 (2007GZS0177); 江西省教育厅科学技术研究项目(GJJ09149); 江西师范大学博士专项研究项目及校管基金项目

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