李東征,謝志春

(華僑大學(xué)廈門工學(xué)院,福建 廈門 361021)

某類調(diào)和映照的Landau定理

李東征,謝志春

(華僑大學(xué)廈門工學(xué)院,福建 廈門 361021)

研究調(diào)和映照的Landau定理和單葉性半徑估計(jì)問題， 首先建立在有界性條件下的調(diào)和映照的系數(shù)估計(jì).在此基礎(chǔ)上，得到一些調(diào)和映照l(shuí)andau定理,改進(jìn)和推廣了先前的結(jié)論.

調(diào)和映照；Landau定理；Schwarz引理

和

1　預(yù)備引理

首先，在有界條件下，得到調(diào)和函數(shù)的系數(shù)估計(jì)，即

同理，我們可以得到

2　主要結(jié)果的證明

因?yàn)閒(0)=0，對(duì)任意z=ρeiθ，有

同理，可得如下推論：

[1]CHENHH,GAUTHIERPM,HENGARTNERW.Blochconstantsforplanarharmonicmappings[J].ProcAmerMathSoc,2000,128:3 231-3 240.

[2]AHLFORSLV.復(fù)分析[M].北京：機(jī)械工業(yè)出版社,2005.

[3]LANDAUE.Derpicard-schottyschesatzunddieblochschekonstanten[M].Berlin:SitzungsberPress，AkadWissBerlinPhys-MathKl,1926：467-474.

[4]CHENHH,GAUTHIERPM.Thelandautheoremandblochtheoremforplanarharmonicandplu-riharmonicmappings[J].ProcAmerMathSoc,2011,139:583-595.

[5]GRIGORYANA.Landauandblochtheoremsforharmonicmappings[J].ComplexVariableTheoryAppl,2006,51(1):81-87.

[6]HUANGXZ.Estimatesonblochconstantsforplanarharmonicmappings[J].JMathAnalAppl,2008,337:880-887.

[7]DORFFM,NOWAKM.Landau’stheoremforplanarharmonicmappings[J].ComputMethFu-nctTheory,2004,4:151-158.

[8]LIUMS.Landau’stheoremforplanarharmonicmappings[J].ComputersandMathematicswithApplications,2009,57(7):1 142-1 146.

[9]李東征,陳行堤.調(diào)和映照的Landau定理[J].華僑大學(xué)學(xué)報(bào):自然科學(xué)版,2012,33(5)：584-589.

[10]劉名生,劉志文,朱玉燦.某類雙調(diào)和映射的Landau型定理[J].數(shù)學(xué)學(xué)報(bào):中文版,2011,54(1):69-80.

[11]GRAHAMI,KOHRG.Geometricfunctiontheoryinoneandhigerdimensions[M].NewYork:Dekker,2003.

(責(zé)任編輯曉軍)

Landau Theorem for Certain Harmonic Mappings

LI Dong-zheng,XIE Zhi-chun

(XiamenInstituteofTechnology,HuaqiaoUniversity,Xiamen361021,China)

InthispaperwestudiedLandautheoremandtheunivalentradiusofaharmonicmapping.Coefficientestimatesfornormalizedplanarharmonicmappingswereprovided,andLandautheoremforharmonicmappingswasinvestigatedonthisbasis.Theresultsimproveandextendtherelatedonesbyearlierauthors.

harmonicmapping;Landautheorem;Schwarzlemma

2014-12-15

2015-02-01

福建省自然科學(xué)基金項(xiàng)目(2014J01013)

李東征(1986-)，女，助教，碩士，研究方向?yàn)閺?fù)分析.E-mall：ldz.16@163.com

O174.55A

1673-4432(2015)01-0098-04