Dirichlet型空间的复合算子.pdf

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3、¼ê˜m.d'p‚5ŽfC':f!f'¡•EÜŽf.©¥,·‚̇lü•¡ïÄDirich-let.˜mDpþEÜŽfk.5,;5;¿•:ïÄDirichlet˜mDþEÜŽfk.5,;59Schattena.©Ù̇•¹±eo‡Ü©:1˜Ù0üþ˜²;¼ê˜m,•)BMOA˜m,Bloch˜m9Dirichlet.˜mÄVg,PÒ9µ•£.1ÙïÄDirichlet.˜mþEÜŽfC'n•x.'1nÙïÄ3Dirichlet.˜mþEÜŽfk.5§;5Nevan-linna.Oê¼ê•x.1oÙïÄ3Dirichlet˜mþE

4、ÜŽf•SchattenaNevan-linna.Oê¼ê•x.'''………ccc:EÜŽf,Nevanlinna.Oê¼ê,Dirichlet.˜m.IöÞŒÆa¬ÆØ©AbstractLetDbetheunitdiscofcomplexplaneand'beaholomorphicmappingfromDtoitself.DenoteH(D)thespaceofallanalyticfunctionsonD,and'inducesacompositionoperatorC':f!f'.Inthisthesis,westudycompositionoperators

5、betweenDirichlet-typespaces.CertaingrowthconditionsforgeneralizedNevanlinnacountingfunc-tionsoftheinducingmapareshowedtothenecessaryandsucientforsuchoperatorstobeboundedorcompact.Therearefourpartsinthisthesisasfollows.Therstchapterisconcernedindenitionsandbackgroundsofsomeclas-sicalfun

6、ctionspacessuchasBMOAspace,theBlochspace,theDirichlettypesapcesDp.Somerelativeresultsaboutthemarealsolisted.Chapter2isaimedatinvestigatingthecompositionoperatorsCfromDp'toDpintermsof'n.Inchapter3,westudythecompositionoperatorsC'onDirichlet-typespaces.Wegivethenecessaryandsucientcondition

7、forcompositionoperatorstobeboundedorcompactintermsofgeneralizedNevanlinnacountingfunctions.Inchapter4,wegivethenecessaryandsucientconditionforcompositionoperatorsonweightedDirichletspacebelongingtoSchattenIdealintermsofgeneralizedNevanlinnacountingfunctions.Keyword