Bloch 型空间的一个刻画.pdf

数 学 杂 志 Vo1．34(2014) No．5 J．ofMath．(PRC) A CHARACTERIZATIoN 0F BLoCH ．TYPE SPACES WANG Xiong-liang (Sch。。lofMathematicn1Sciences，Chuzh。uUniversity，Chuzh。u239000，Chin。) Abstract：Inthispaper，weinvestigatethepropertiesoffunctionsintheBloch．typespaces ． Byusingthepseudo—hyperbolicmetricandsomeinequalities，weobtainanew characterizationof Bloch—typespaces召“(Bn)with0 1，whichgeneralizestheHolland。Walshcharacterization inahigherorderversionforBloch-typespaces (皿 )． Keywords： Bloch-typespaces；Holland—W alshcharacterizati0n：thepseudo—hyperbolicmet． ric 2010MR SubjectClassification： 32A18 Documentcode： A ArticleID： 0255．7797(2014)05．0843．06 1 Introduction LetBnbetheunitballinthen—dimensionalcomplexEuclideanspaceC ．For0 n ∞，theBloch—typespace (Bn)consistsofholomorphicfunctionsfinBnsuchthat sup(1—1zl。)IVf(z)I∞ ∈Bn orequivalently sup(1一izl。)f，()fO0， z∈Bn o whereV／()=(等()，…，‰oL(z))andRf() _ 2／()·TheB1。ch—typespace 。(Bn)becomesaBanachspacewiththenorm flIBa(璐)=Il厂(0)I+sup(1一lzl。)[V／(z)l，f∈B (B) ∈B礼 When =1， ( )isclassicalBlochspace召( )．ForthegeneraltheoryofBloch—type spaceswereferto[1]and[2]．TheZygmundclassA1(Bn)isthespaceofholomorphic functionsin whosefirstorderpartialderivativesareintheBlochspace n)．Seepage 246of[2】． Received date：2012—07-15 Accepted date：201