[1]朱剑峰.调和K-拟共形映照下Heinz不等式的精确估计[J].华侨大学学报(自然科学版),2014,35(3):354-357.[doi:10.11830/ISSN.1000-5013.2014.03.0354]
　ZHU Jian-feng.A Sharp Estimate for Heinz’s Inequality of Harmonic K-Quasiconformal Mappings[J].Journal of Huaqiao University(Natural Science),2014,35(3):354-357.[doi:10.11830/ISSN.1000-5013.2014.03.0354]
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调和K-拟共形映照下Heinz不等式的精确估计()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第35卷
期数:
2014年第3期
页码:
354-357
栏目:
出版日期:
2014-05-16

文章信息/Info

Title:
A Sharp Estimate for Heinz’s Inequality of Harmonic K-Quasiconformal Mappings
文章编号:
1000-5013(2014)03-0354-04
作者:
朱剑峰
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
ZHU Jian-feng
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
调和拟共形映照;  Heinz不等式;  Hübner不等式;  调和测度;  测度拟不变性
Keywords:
harmonic quasiconformal mapping;  Heinz inequality;  Hubner inequality;  harmonic measure;  quasi-invariance measure
分类号:
O174.2
DOI:
10.11830/ISSN.1000-5013.2014.03.0354
文献标志码:
A
摘要:
设w=P［F］(z)为单位圆到自身上的调和拟共形映照,满足w(0)=0,其中F(exp(it))=exp(iγ(t))为边界函数. 利用调和测度的拟不变性得到边界函数的一个偏差估计,进而利用改进的Hübner不等式得到调和拟共形映照下Heinz不等式的一个精确估计.
Abstract:
Assume that w=P［F］(z)is a harmonic quasiconformal self-mapping of the unit disk satisfying w(0)=0, where F(exp(it))=exp(iγ(t))is the boundary function. By using the quasi-invariance of harmonic measure, we obtain an estimate for the boundary function. Furthermore, applying the improved Hübner inequality we obtain a sharp estimate of Heinz’s inequality for harmonic quasiconformal mappings.

参考文献/References:

[1] DUREN P.Harmonic mappings in the plane[M].New York:Cambridge University Press,2004:6-7.
[2] LEWY L. On the non-vanishing of the Jocobian in certain one-to-one mappings[J]. Bull Am Math Soc, 1932,42(10):689-692.
[3] KALAJ D.Quasiconformal and harmonic mappings between Jordan domains[J].Mayh Z,2008,260(2):237-252.
[4] PARTYKA D,SAKAN K.On an asymptotically sharp variant of Heinz’s inequality[J].Ann Acad Sci Fenn Math,2005,30:167-182.
[5] MIROSLAV P.Boundary correspondence under harmonic quasiconformal homeomorphisma of the unit disk[J].Ann Acad Sci Fenn Math,2002,27(2):365-372.
[6] QIU Song-liang,REN Liang-yu.Sharp estimate for Hübner’s upper bound function with applications[J].Appl Math J Chinese Univ,2010,25(2):227-235.
[7] 朱剑峰.单位圆盘上调和拟共形映照的复特征估计[J].华侨大学学报:自然科学版,2010,31(4):476-479.
[8] 朱剑峰,黄心中.两类调和函数的拟共形性质[J].华侨大学学报:自然科学版, 2011,32(6):705-709.
[9] ZHU Jian-feng,ZENG Xiao-ming.Estimate for Heinz inequality in the small dilatation of harmonic quasiconformal mappings[J].Journal of Computational Analysis and Applications,2011,13(6):1081-1087.
[10] 朱剑峰.单位圆到凸区域上的调和拟共形映照[J].数学进展,2012,41(1):50-54.
[11] HEINZ E.Über die lösungen der minimalflächengleichung[J].Nachr Akad Wiss Math-Phys KI,1952,2:51-56.
[12] HALL R R.On an inequality of Heina[J].J Analyse Math,1982,42(1):185-198.

备注/Memo

备注/Memo:
收稿日期: 2013-07-15
通信作者: 朱剑峰(1980-),男,讲师,主要从事函数论的研究.E-mail:flandy@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11101165)
更新日期/Last Update: 2014-05-20