非交換Orlicz空間的研究.pdf

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2、·?O?ê'X?nú5.31!￥,·'uOrliczm?SN.31n!￥,·y2Orlicz-HardymSzeg¨oúRiesz.?)?n.31o!￥??f?)?n.1nü?·?ky2^?"E?5§ùgy2,fêAkLΦ-?)=A′géfê.,?géfêA.1oü?￥·??Orliczmy2???n,Young?aúClarkson-McCarthy?a.'cμO(píng)?ê,Orliczm,Orlicz-Hardym,Orliczm.iEnglishAbstractThisthesisisdevotedtostud

3、ythenoncommutativeOrliczspacesandwhichisdividedintofoursectionsandstatedasfollows:Inthe?rstsection,wegivetheresearchstatusandpresentsomenotationstogetherwithde?nitions.Insectiontwo,weconsidertherelationshipsofgrowthfunctionsandsomepropertiesofthefunctions,somebasicresultsofnoncommu

4、tativeOrliczspacesassociatedwithgrowthfunctionsandN-functions,theSzeg¨oandRiesztypefactorizationtheoremsofnoncommu-tativeOrlicz-Hardyspacesandinner-outerfactorizationsfornoncommutativeOrlicz-Hardyspaces.Insectionthree,weprovedcontractivityofconditionalexpectationEandtracialsubal-ge

5、braAofMhasLΦ-factorizationifandonlyifAisasubdiagonalalgebra.Wealsogivesomecharacterizationsofsubdiagonalalgebras.Insectionfour,westudythenoncommutativeOrliczmodularspacesassociatedwithgrowthfunctions.Weprovedominatedconvergencetheorems,YounginequalitiesandClarkson-McCarthyinequalit

6、iesforthisspaces.Keywords:growthfunctions,noncommutativeOrliczspaces,noncommutativeOrlicz-Hardyspaces,noncommutativeOrliczmodularspace.ii8881111SSSóóó.................................................................................11.1??μ...........................................

7、................................11.2??ì(J......................................................................21.3y￡...........................................................................52Orlicz-Hardymmmnnn???....................................................92.1úó.....

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