[1]李西振,陈行堤.Bloch型双调和映照[J].华侨大学学报(自然科学版),2017,38(5):737-741.[doi:10.11830/ISSN.1000-5013.201609021]
 LI Xizhen,CHEN Xingdi.On Biharmonic Bloch-Type Mappings[J].Journal of Huaqiao University(Natural Science),2017,38(5):737-741.[doi:10.11830/ISSN.1000-5013.201609021]
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Bloch型双调和映照()
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《华侨大学学报(自然科学版)》[ISSN:1000-5013/CN:35-1079/N]

卷:
第38卷
期数:
2017年第5期
页码:
737-741
栏目:
出版日期:
2017-09-20

文章信息/Info

Title:
On Biharmonic Bloch-Type Mappings
文章编号:
1000-5013(2017)05-0737-05
作者:
李西振 陈行堤
华侨大学 数学科学学院, 福建 泉州 362021
Author(s):
LI Xizhen CHEN Xingdi
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
Bloch函数 双调和映照 系数估计 拟正则映照
Keywords:
Bloch function biharmonic mapping coefficient estimate quasiregular mapping
分类号:
O174.55
DOI:
10.11830/ISSN.1000-5013.201609021
文献标志码:
A
摘要:
研究 Bloch 型双调和函数的判别准则和系数估计.通过建立双调和函数的线性和复合性质,得到双调和函数的 Bloch 型判别法则.利用双调和的表示理论及调和函数的 Pre-Schwarz 导数估计,给出 Bloch 型双调和函数的单叶性判定定理及系数估计.
Abstract:
This paper studies the criterion and coefficient estimate of Bloch-type biharmonic mappings. After establishing the linear and composite properties of biharmonic mappings, we give a criterion for biharmonic mappings to be Bloch-type. Combining the representation theorem of the biharmonic mappings with the estimation of Pre-Schwarz derivative of harmonic mappings, we obtain a univalent criterion and some coefficient estimates of biharmonic mappings for Bloch-type biharmonic mappings.

参考文献/References:

[1] LEWY H.On the non-vanishing of the Jacobian in certain one-to-one mappings[J].Bulletin of the American Mathematical Society,1936,42(10):689-698.
[2] DUREN P.Harmonic univalent functions[M].Cambridge:Cambridge University Press,2004:1-17.
[3] CLUNIE J,SHEIL-SMALL T.Harmonic univalent functions[J].Ann Acad Sci Fenn Ser A,1984,9(1):3-25.
[4] ABDULHADI Z,MUHANNA Y,KHURI S.On univalent solutions of the biharmonic equation[J].J Inequal Appl,2005,5(2005):469-478.
[5] KALAJ D.On quasiregular mappings between smooth Jordan domains[J].Journal of Mathematical Analysis and Applications,2010,362(1):58-63.
[6] AHLFORS L V,EARLE C J.Lectures on quasiconformal mappings[M].New York:American Mathematical Society,1966:21-34.
[7] ANDERSON J M,CLUNIE J,POMMERENKE C.On Bloch functions and normal functions[J].J Reine Angew Math,1974,270:12-37.
[8] DANIKAS N.Some Banach spaces of analytic functions, function spaces and complex analysis, joensuu[J].Univ Joensuu Dep Math Rep Ser,1997,2:9-35.
[9] POMMERENKE C.On Bloch functions[J].J London Math Soc,1970,2(2):689-695.
[10] EFRAIMIDIS I,GAONA J,HERNÁNDEZ R,et al.On harmonic Bloch-type mappings arXiv preprint arXiv[DB/OL].[2016-07-15] [2016-09-05] .https://arxiv.org/pdf/1607.04626v1.pdf.
[11] POMMERENKE C.Boundary behaviour of conformal maps[M].Berlin:Springer-Verlag,1992:185-187.
[12] SEIDEL J,WALSH L.On the derivatives of functions analytic in the unit circle and their radii of univalence and of p-valence[J].Trans Amer Math Soc,1942,52(1):128-216.
[13] ZHU K. Operator theory in function spaces, marcel dekker[M]. New York: American Mathematical Soc,2007:101-132.
[14] HERNÁNDEZ R,MARTÍN M J.Pre-Schwarzian and Schwarzian derivatives of harmonic mappings[J].J Geom Anal,2015,25(1):64-91.
[15] BEARDON A,MINDA D.The hyperbolic metric and geometric function theory[J].Quasiconformal Mappings and Their Applications,2007,3:9-56.

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备注/Memo

备注/Memo:
收稿日期: 2016-09-15
通信作者: 陈行堤(1976-),男,教授,博士,主要从事函数论的研究.E-mail:chxtt@hqu.edu.cn.
基金项目: 国家自然科学基金资助项目(11471128); 福建省自然科学基金计划资助项目(2014J01013); 华侨大学青年教师科研提升资助计划(ZQN-YX110); 华侨大学研究生科研创新能力培育计划资助项目(1511313003)
更新日期/Last Update: 2017-09-20