| 调和映照的双Lipschitz性质 |
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| 引用本文： | 朱剑峰.调和映照的双Lipschitz性质[J].数学年刊A辑(中文版),2018,39(1):33-42. |
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| 作者姓名： | 朱剑峰 |
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| 作者单位： | 华侨大学数学科学学院 |
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| 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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| 摘 要： | 设w(z)为单位圆盘U到约当区域Ω?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Ω为有界凸区域,对其边界函数给出一个较弱的条件,使得w=Pf](z)为调和拟共形映照.
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| 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 |
| 收稿时间： | 2015/8/19 0:00:00 |
| 修稿时间： | 2016/3/4 0:00:00 |
Bi-Lipschitz Properties for Harmonic Mappings |
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| ZHU Jianfe.Bi-Lipschitz Properties for Harmonic Mappings[J].Chinese Annals of Mathematics,2018,39(1):33-42. |
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| Authors: | ZHU Jianfe |
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| Institution: | School of Mathematical Sciences, Huaqiao University,
Quanzhou 362021, \linebreak Fujian, China. |
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| Abstract: | 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 $w(z)=Pf](z)$ is a harmonic quasiconformal mapping. |
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| Keywords: | Harmonic mappings Harmonic quasiconformal mappings Bi-Lipschitz condition $H^p$ space $h^p$ space |
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