一类解析函数空间上的Toeplitz算子

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1、汕头大学硕士学位论文一类解析函数空间上的Toeplitz算子姓名：姚炳洪申请学位级别：硕士专业：基础数学指导教师：娄增建2010-06Á‡éuEÿÝ,>0,Úb2L1,½ÂToeplitzŽfXe:Z(1jwj2)1b(w)T(b)(z)=d(w):D(1wz)+1Z.J.Wu,R.H.ZhaoÚN.Zorboska‰ÑToeplitzŽfT3Bloch.˜mþ´k.½;˜‡d•x.©3˜a)Û¼ê˜mþ•Äaq¯K,)ûToeplitzŽf3Ùþk.5Ú;5,(Jí2Z.J

2、.Wu,R.H.ZhaoÚN.Zorboska(Ø"©©•üÜ©.1˜Ü©X•0ToeplitzŽf,Bloch.˜mÚ˜a)Û¼ê˜m½Â±9˜ƒ'Ä:•£Ú®k(Ø.1Ü©

3、^SÈ5Ÿ‰ÑToeplitzŽf3˜a)Û¼ê˜mþ´k.½;d•x.'…c:ToeplitzŽf,)Û¼ê˜m,Bloch.˜m.AbstractForacomplexmeasure,>0,andb2L1,deneaToeplitzoperatorasfollows:Z(1jwj2)1b(w)T

4、(b)(z)=d(w):D(1wz)+1Z.J.Wu,R.H.ZhaoandN.ZorboskacharacterizedcomplexmeasursesforwhichtheToeplitzoperatorTisboundedorcompactonBloch-typespaces.Inthisthesis,weextendtheresulttoaclassofanalyticfunctionsandcharacterizecomplexmeasursesforwhichtheToeplit

5、zoperatorTisboundedorcompactonthespace.Thethesisisdividedtwoparts.TherstpartprovidesthedenitionsofToeplitzoperator,Bloch-typespacesandaclassofanalyticfunctions.Thepreliminariesandrelatedknownresultsarealsoprovided.Thesecondpartgivesnecessaryandsucie

6、ntconditionsfortheToeplitzoperatorTtobeboundedorcompactontheclassofanalyticfunctionsbyusingpropertyoftheinnerproduct.KeyWords.Toeplitzoperator,analyticfunctionspaces,Bloch-typespaces.ÆØ©M5(²Ø©´·‡<3“•e?1óŠïÄ9ïĤJ.Ø©¥ØAO±I5Ú—/•,Ø•¹Ù¦<½Ù§Å®²uL

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