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1、Bloch函数和小Bloch函数判别准则的推广第24卷第3期2006年8月贵州师范大学(自然科学版)JournalofGuizhouNormalUniversity(NaturalSciences)Vo1.24.No.3Aug.2006文章编号:1004--5570(2006)03—0o84—04Ageneralizati0nofafunctionsandlittlecriterionofBlochBlochfunctionsYANGCong—li.WUPeng—cheng(SchoolofMathe
2、maticsandComputerScience,GuizhouNormalUniversity,Guiyang,Guizhou550001,China)Abstract:Inthispaper,weinvestigatethecriterionofBlochfunctionandlittleBlochfunction,weob—tainanextendedresultsofAulaskari—Lappan,Minda,Aulaskari—WulanandWu.Keywords:Blochfuncti
3、on;littleBloehfunctionBloch函数和小Bloch函数判别准则的推广杨丛丽,伍鹏程(贵州师范大学数学与计算机科学学院,贵州贵阳550001)摘要:研究了Bloch函数和小Bloch函数的判别准则,并且推广了Aulaskari-lappan,Minda,Aulaskari-Wulan和Wu的结果.关键词:Bloch函数;小Bloch函数中图分类号:0174文献标识码:A1IntroductionLetA={z:lzl<1}betheunitdiskinthecomplexpl
4、ane.ananalyticfunctionfintheunitdiskAiSsaidtobeaBlochfunction.ifitsatisfiessuP(I—Izl)l厂z)l<∞.AnanalyticfunctionfintheunitdiskAiscalledalittleBloehfunctioniflim.+l(1一Izl)If(z)l=0-AulaskariandLappan[】andMinda[】gaveanMtemafivecharacterizationofBloehfunc
5、tions.TheyprovedthefollowingTheoremALM:AfunctionfanalyticintheU—nitdiskAisnotaBlochfunctionifandonlyifthereexistasequence{z}cAwithlzl---~1,andase—quence{P}ofpositivenumberssatisfying_,suchthatthesequencetf(z+p)-f()}convergeslocallyuniformlytoanonconstan
6、tanalyticfunctioninC.ForlittleBloehfunctions,AulaskariandWu-lan[】provedthe~llowing收稿日期:2006—03—28基金项目:ResearchsupportedbythegovernorfoundationofGuizhouprovince[02No.1]andGuizhouspecialoutstandingscientistfoundation.作者简介:YangCongli(1981一),Female,bominLip
7、ing,Guizhou,graduatestudent,majorintheo~offunction.84第3期杨丛丽,伍鹏程:Bloeh函数和小Bloeh函数判别准则的推广TheoremAW:AfunctionfanMyticontheunitdiskAisnotahttleBlochfunctionifandonlyifthereexistaconstantR>0,asequence{:}cAwithIzI---~1,andasequence{P}ofpositivenum—bersSati
8、sng<1,suchtllatthese—quence{,(:+p)-f(z)}convergeslocallyuni—formlytoanonconstantanalyticfunctioninIl<R.2MainresultandProofWeinvestigatethepossibilityofintroducingaslidingscaleinvolvingaparameterintothesetheoremsinanalogytoP
