[1]谢志春,黄心中.一类Nehari函数族的拟共形延拓与系数偏差[J].华侨大学学报(自然科学版),2011,32(3):343-347.[doi:10.11830/ISSN.1000-5013.2011.03.0343]
　XIE Zhi-chun,HUANG Xin-zhong.On the Quasiconformal Extensions and Coefficients Distortion for a Nehari Class[J].Journal of Huaqiao University(Natural Science),2011,32(3):343-347.[doi:10.11830/ISSN.1000-5013.2011.03.0343]
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一类Nehari函数族的拟共形延拓与系数偏差()
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《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第32卷
期数:
2011年第3期
页码:
343-347
栏目:
出版日期:
2011-05-20

文章信息/Info

Title:
On the Quasiconformal Extensions and Coefficients Distortion for a Nehari Class
文章编号:
1000-5013(2011)03-0343-05
作者:
谢志春; 黄心中
华侨大学数学科学学院
Author(s):
XIE Zhi-chun;  HUANG Xin-zhong
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Nehari函数族;  Schwarz导数;  拟共形延拓;  系数估计
Keywords:
Nehari class;  Schwarzian derivative;  quasiconformal extension;  coefficient estimate
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.2011.03.0343
文献标志码:
A
摘要:
研究一类Nehari函数族的拟共形延拓,给出拟共形延拓的复伸张估计.对该类函数在单位圆内级数展开的系数给出一些精确估计,改进并推广了杨宗信等人的相应结果.
Abstract:
The quasiconformal extensions for one class of Nehari functions are considered,and their dilatations are estimated.Some sharp coefficient estimates are obtained for these Nehari functions with normal condition.Our results improve the one made by Yang and Chen.

参考文献/References:

[1] NEHARI Z. The Schwarzian derivative and schlicht functions [J]. Bulletin of the American Mathematical Society, 1949(6):545-551.doi:10.1090/S0002-9904-1949-09241-8.
[2] AHLFORS L, WEILL G. A uniqueness theorem for Beltrami equations [J]. Proceedings of the American Mathematical Society, 1962.975-978.doi:10.1090/S0002-9939-1962-0148896-1.
[3] NEHARI Z. Univalence criteria depending on the Schwarzian derivative [J]. Illinois Journal of Mathematics, 1979(3):345-351.
[4] GEHRING F W, POMMERENKE C. On the Nehari univalence criterion and quasicircles [J]. Commentarii Mathematici Helvetici, 1984(1):226-242.doi:10.1007/BF02566347.
[5] CHUAQUI M, OSGOOD B. Finding complete conformal metrics to extend conformal mappings [J]. Indiana University Mathematics Journal, 1998(4):1273-1291.doi:10.1512/iumj.1998.47.1606.
[6] CHUAQUI M, OSGOOD B. Sharp distortion theorems asociated with the Schwarzian derivative [J]. Journal of the London Mathematical Society, 1993(2):289-298.doi:10.1112/jlms/s2-48.2.289.
[7] CHUAQUI M, POMMERENKE C. Characteristic properties of Nehari functions [J]. Pacific Journal of Mathematics, 1999(1):83-94.doi:10.2140/pjm.1999.188.83.
[8] CHUAQUI M, OSGOOD B. General univalence criteria in the disk:Extensions and extremal function [J]. Annales Academiae Scientiarum Fennicae, 1998(1):101-132.
[9] CHUAQUI M, OSGOOD B. Ahlfors-Weill extensions of conformal mappings and critical points of the Poincaré metric [J]. Commentarii Mathematici Helvetici, 1994(1):659-668.doi:10.1007/BF02564508.
[10] LEHTO O. Univalent functions and Teichmüller space [M]. New York:springer-verlag, 1987.
[11] 杨宗信, 陈纪修. Nehari函数族的偏差定理与拟共形延拓 [J]. 数学年刊A辑, 2004(6):695-704.doi:10.3321/j.issn:1000-8134.2004.06.002.
[12] 杨宗信. 一类Nehari函数的偏差性质 [J]. 数学年刊A辑, 2007(6):781-790.doi:10.3321/j.issn:1000-8134.2007.06.005.

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备注/Memo

备注/Memo:
福建省自然科学基金项目(2008J0195)
更新日期/Last Update: 2014-03-23