| 朱剑峰.调和映照的双Lipschitz性质[J].数学年刊A辑,2018,39(1):33~42 |
| 调和映照的双Lipschitz性质 |
| Bi-Lipschitz Properties for Harmonic Mappings |
| Received:August 19, 2015 Revised:March 04, 2016 |
| DOI：10.16205/j.cnki.cama.2018.0004 |
| 中文关键词: 调和映照, 调和拟共形映照, 双Lipshcitz条件, $H^p$空间, $h^p$空间 |
| 英文关键词:Harmonic mappings, Harmonic quasiconformal mappings,Bi-Lipschitz condition, $H^p$ space, $h^p$ space |
| 基金项目:本文受到国家自然科学基金 (No.11501220, No.11471128),
福建省自然科学基金(No.2016J01020)和华侨大学中青年教师科研提升计划
(No.ZQN-YX110)的资助. |
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| 中文摘要: |
| 设$w(z)$为单位圆盘$\mathbf{U}$到约当区域$\Omega\subseteq \mathbf{C}$上的
调和映照. 给出$w(z)$具有Lipschitz性质的等价条件. 进一步地,
若$\Omega$为有界凸区域, 对其边界函数给出一个较弱的条件,
使得$w=P[f](z)$为调和拟共形映照. |
| 英文摘要: |
| Suppose that $w(z)$ is a harmonic mapping of the unit disk
$\mathbf{U}$ onto a Jordan domain $\Omega\subseteq \mathbf{C}$. The author finds
some equivalent conditions for the Lipschitz property of $w(z)$. Moreover,
if $\Omega$ is a bounded convex domain, a weaker condition on the
boundary function $f$ is found, such that $w(z)=P[f](z)$ is a harmonic quasiconformal mapping. |
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