[1]王朝祥.Beurling-Ahlfors扩张伸张函数的估计[J].华侨大学学报(自然科学版),2009,30(1):108-110.[doi:10.11830/ISSN.1000-5013.2009.01.0108]
　WANG Chao-xiang.Estimates of the Dilatation Function for Beurling-Ahlfors Extension[J].Journal of Huaqiao University(Natural Science),2009,30(1):108-110.[doi:10.11830/ISSN.1000-5013.2009.01.0108]
点击复制

Beurling-Ahlfors扩张伸张函数的估计()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第30卷
期数:
2009年第1期
页码:
108-110
栏目:
出版日期:
2009-01-20

文章信息/Info

Title:
Estimates of the Dilatation Function for Beurling-Ahlfors Extension
文章编号:
1000-5013(2009)01-0108-03
作者:
王朝祥
华侨大学数学科学学院
Author(s):
WANG Chao-xiang
School of Mathematics Seiences, Huaqiao University, Quanzhou 362021, China
关键词:
拟共形映照;  Beurling-Ahlfors扩张;  伸张函数;  拟对称函数
Keywords:
quasiconformal mapping;  Beurling-Ahlfors extension;  dilatation function;  quasisymmetric function
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2009.01.0108
文献标志码:
A
摘要:
设h(x)是实轴上的保向同胚,满足h(±∞)=±∞.当h(x)的拟对称函数ρ(x,t)被递减函数ρ(t)所控制时,h(x)的Beurling-Ahlfors扩张的伸张函数具有以下估计:当ρ*≥45时,D≤2ρ*; 而当1≤ρ*<45时,D≤2ρ*+21ρ*.其中,ρ*=ρ(2y).
Abstract:
Let h be a homeomorphism of R onto itself with h(±∞)=±∞,when the quasisymmetric function ρ(x,t) of h is controled by a decreasing function ρ(t),the dilatation function D obtained by the Beurling-Ahlfors extension of h is further estimated as follows: if ρ*≥45,then D≤2ρ*,and if 1≤ρ*<45,then D≤2ρ*+12ρ*,where ρ*=ρ(y2).

参考文献/References:

[1] BEURLING A, AHLFORS L. The boundary correspondence under quasiconformal mappings [J]. Acta Mathematica, 1956.125-142.doi:10.1007/BF02392360.
[2] AHLFORS L V. Lectures on quasiconformal mappings [M]. Princeton:Van Nostrand, 1966.
[3] LEHTINEN M. The dilatation of Beurling-Ahlfors extension of quasisymmetric functions [J]. Annales Academiae Scientiarum Fennicae Series AI Mathematica, 1983.187.
[4] 方爱农. 广义Beurling-Ahlfors 定理 [J]. 中国科学E辑, 1995(6):565-572.
[5] CHEN Ji-xiu, CHEN Zhi-guo, HE Cheng-qi. The boundary correspondence under μ(z)-homeomorphisms [J]. Michigan Mathematical Journal, 1996.211.doi:10.1307/mmj/1029005458.
[6] 郑学良, 方爱农. 伸张函数增长阶的估计 [J]. 数学进展, 2003(5):591.doi:10.3969/j.issn.1000-0917.2003.05.010.
[7] 郑学良, 王洁. 关于伸张函数估计的一点注记 [J]. 台州学院学报, 2004(3):1-5.doi:10.3969/j.issn.1672-3708.2004.03.001.

相似文献/References:

[1]赖万才.拟共形映照的模数偏差[J].华侨大学学报(自然科学版),1985,6(2):141.[doi:10.11830/ISSN.1000-5013.1985.02.0141]
　Lai Wancai.On the Distortion of Modulus of Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),1985,6(1):141.[doi:10.11830/ISSN.1000-5013.1985.02.0141]
[2]赖万才.拟共形映照的一个极值问题[J].华侨大学学报(自然科学版),1989,10(4):359.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
　Lai Wancai.An Extremal Problem for Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),1989,10(1):359.[doi:10.11830/ISSN.1000-5013.1989.04.0359]
[3]黄心中.参数表示下的拟共形映照[J].华侨大学学报(自然科学版),1997,18(2):111.[doi:10.11830/ISSN.1000-5013.1997.02.0111]
　Huang Xinzhong.Quasiconformal Mappings with Parametric Representation[J].Journal of Huaqiao University(Natural Science),1997,18(1):111.[doi:10.11830/ISSN.1000-5013.1997.02.0111]
[4]黄心中.分段与整体拟对称函数之间的关系[J].华侨大学学报(自然科学版),1999,20(1):1.[doi:10.11830/ISSN.1000-5013.1999.01.0001]
　Huang Xinzhong.Relation between Piecewise and Global Quasi Symmetric Functions[J].Journal of Huaqiao University(Natural Science),1999,20(1):1.[doi:10.11830/ISSN.1000-5013.1999.01.0001]
[5]刘金雄.Reich的一个定理改进及其相关问题[J].华侨大学学报(自然科学版),2000,21(1):8.[doi:10.3969/j.issn.1000-5013.2000.01.002]
　Liu Jinxiong.Improving One of Reich’s Theorems and Problem Correlated with It[J].Journal of Huaqiao University(Natural Science),2000,21(1):8.[doi:10.3969/j.issn.1000-5013.2000.01.002]
[6]刘金雄.一类唯一极值Teichmǖller映照的判别法[J].华侨大学学报(自然科学版),2000,21(4):331.[doi:10.3969/j.issn.1000-5013.2000.04.001]
　Liu Jinxiong.Criterion for a Class of Uniquely Extremal Teichmüller Mappings[J].Journal of Huaqiao University(Natural Science),2000,21(1):331.[doi:10.3969/j.issn.1000-5013.2000.04.001]
[7]刘金雄.一类唯一极值Teichmller映照的存在性[J].华侨大学学报(自然科学版),2001,22(1):6.[doi:10.3969/j.issn.1000-5013.2001.01.002]
　Liu Jinxiong.Existence of a Class of Uniquely Extremal Teichmller Mappings[J].Journal of Huaqiao University(Natural Science),2001,22(1):6.[doi:10.3969/j.issn.1000-5013.2001.01.002]
[8]陈行堤,黄心中.拟共形映照的爆破集问题[J].华侨大学学报(自然科学版),2001,22(2):111.[doi:10.3969/j.issn.1000-5013.2001.02.001]
　Chen Xingdi,Huang Xinzhong.Explodable Set of Quasiconformal Mapping[J].Journal of Huaqiao University(Natural Science),2001,22(1):111.[doi:10.3969/j.issn.1000-5013.2001.02.001]
[9]朱剑锋,黄心中.区间上拟对称函数的延拓定理[J].华侨大学学报(自然科学版),2007,28(1):83.[doi:10.3969/j.issn.1000-5013.2007.01.022]
　ZHU Jian-feng,HUANG Xin-zhong.The Extension Theorem of Quasisymmetric Function on the Interval[J].Journal of Huaqiao University(Natural Science),2007,28(1):83.[doi:10.3969/j.issn.1000-5013.2007.01.022]
[10]林珍连.关于“Beurling-Ahlfors扩张的推广”一文的一点注[J].华侨大学学报(自然科学版),2007,28(3):335.[doi:10.3969/j.issn.1000-5013.2007.03.029]
　LIN Zhen-lian.A Note on the Paper of the Generalization of Beurling-Ahlfors′ Extension[J].Journal of Huaqiao University(Natural Science),2007,28(1):335.[doi:10.3969/j.issn.1000-5013.2007.03.029]
[11]林峰.Beurling-Ahlfors扩张的伸张函数的边界极限[J].华侨大学学报(自然科学版),2004,25(4):352.[doi:10.3969/j.issn.1000-5013.2004.04.004]
　Lin Feng.Boundary Limit of Dilatation Function of Beurling-Ahlfors Extension[J].Journal of Huaqiao University(Natural Science),2004,25(1):352.[doi:10.3969/j.issn.1000-5013.2004.04.004]

备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511025)
更新日期/Last Update: 2014-03-23