| 徐庆华,刘太顺,徐辉明.一类多复变全纯映照子族的增长和偏差定理[J].数学年刊A辑,2014,35(5):565~574 |
| 一类多复变全纯映照子族的增长和偏差定理 |
| Growth and Distortion Theorems for a Subclass of Holomorphic Mappings in SeveralComplex Variables |
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| DOI： |
| 中文关键词: 增长定理, 偏差定理, 星形映照的子族 |
| 英文关键词:Growth theorem, Distortion theorem, Subclasses of starlike mappings |
| 基金项目:国家自然科学基金
(No.10971063, No.11061015, No.11031008),
江西省自然科学基金 (No.2010GZS0096), 浙江省自然科学基金 (No.Y6110053)和
江西省教育厅基金 (No.GJJ09149) |
| Author Name | Affiliation | E-mail | | XU Qinghua | College of Mathematics and Information Science, Jiangxi
Normal
University, Nanchang 330022, China. | xuqh@mail.ustc.edu.cn | | LIU Taishun | Department of Mathematics, Huzhou Teachers
College, Huzhou 313000, Zhejiang, China. | lts@ustc.edu.cn | | XU Huiming | College of Mathematics Physics and Information Technology, Zhejiang Normal University, Jinhua 321004, Zhejiang, China. | xhm@zjnu.cn |
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| 中文摘要: |
| 在一般复 Banach 空间 $X$ 中的单位球 $B$上引入一类全纯映照族 $\mathcal{M}_g$. 考虑 $B$ 上满足条件$(Df(x))^{-1}f(x)\in \mathcal{M}_g$的正规化局部双全纯映照
$f(x)$ (其中 $x=0$ 是 $f(x)-x$ 的 $k+1$ 阶零点)并得到其增长定理. 作为应用, 也得到了$\mathbb{C}^n$ 中单位多圆柱 $D^n$ 上映照 $f$ 关于 Jacobi 矩阵
$J_f(z)$ 的偏差定理, 该结果统一和推广了星形映照许多子族的相应结论. |
| 英文摘要: |
| Let $X$ be a complex Banach space with norm
$\|\cdot\|$, $B$ the unit ball in $X$. A class of holomorphic mappings $\mathcal{M}_g$ on $B$ is introduced.
Let $f(x)$ be a normalized locally biholomorphic mappings on $B$
such that $(Df(x))^{-1}f(x)\in \mathcal{M}_g$ (where $x=0$ is the zero of order $k+1$ of $f(x)-x).$ The authors investigate the growth theorem for $f(x)$. As applications, the distortion theorems for the Jacobian matrix $J_f(z)$ are
obtained, where $f(z)$ belongs to the subclasses of starlike mappings defined on the unit polydisc $D^n$ in $\mathbb{C}^n$. These results unify and generalize the corresponding results of many subclasses of starlike mappings. |
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