| 刘太顺,卢金,王建飞.多复变数准凸映射的偏差定理[J].数学年刊A辑,2011,32(5):607~612 |
| 多复变数准凸映射的偏差定理 |
| Distortion Theorems of Quasi-convex Mappings in Several Complex Variables |
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| DOI： |
| 中文关键词: 准凸映射 偏差定理 增长定理 Banach空间 |
| 英文关键词:Quasi-convex mappings Distortion theorem Growth theorem Banach space |
| 基金项目:国家自然科学基金(No.10971063,No.11001246,No.11031008,No.11101139); 浙江省自然科学基金(No.D7080080,No.Y6090694,No.Y6110260,No.Y6110053,No.Y6090036,No.Y6100219)资助的项目 |
| Author Name | Affiliation | E-mail | | LIU Taishun | Department of Mathematics,Huzhou Teachers College,Huzhou 313000,Zhejiang,China. | lts@ustc.edu.cn | | LU Jin | Department of Mathematics,Huzhou Teachers College,Huzhou 313000,Zhejiang,China. | lujin@mail.ustc.edu.cn | | WANG Jianfei | College of Mathematics Physics and Information Technology,Zhejiang Normal University,Jinhua 321004,China. | wangjf@mail.ustc.edu.cn |
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| 中文摘要: |
| 首先给出了 ${\mathbb{C}}^n$ 中单位多圆柱 $D^n$ 上 准凸映射 $f$
关于Jacobin 矩阵 $J_f(z)$ 的偏差定理.
该定理是单位圆盘凸函数的偏差定理在多复变中的推广. 其次得到了
Banach 空间单位球上准凸映射的偏差定理的上界. 最后
给出了关于准凸映射偏差定理的两个猜想. |
| 英文摘要: |
| Firstly,
the authors are concerned with the distortion theorem for the Jacobian
matrix $J_f(z)$ in the case of quasi-convex mapping $f$ on the unit
polydisc $D^n$ in ${\mathbb{C}}^n$. The result is a new
generalization to the case of several complex variables of the well-known distortion
theorem for convex functions of the unit disc.
Secondly, the authors obtain the upper bound estimate of the distortion theorem
for quasi-convex mappings on the unit ball of a complex Banach
space. Finally, two conjectures are given for quasi-convex
mappings on the unit polydisc as well as on the unit ball of a
complex Banach space. |
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