BH_27p_与BL_27p_空间上的某些性质

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1、青岛大学硬士学位论文学位论文独创性声明本人声明，所里交的学位论文系本人在导师指导下独立完成的研究成果。文中依法引用他人的成果，均已做出明确标注或得到许可．论文内容未包含法律意义上已属于他人的任何形式的研究成果，也不包含本人已用于其他学位申请的论文或成果．本人如违反上述声明，愿意承担由此引发的一切责任和后果。敝储貅赫南日期：加吣7年‘月7日35青岛大学硕士学位论文学位论文知识产权权属声明本人在导师指导下所完成的学位论文及相关的职务作品，知识产权归属学校。学校享有以任何方式发表、复制、公开阅览、借阅以及申请专利等权利．

2、本人离校后发表或使用学位论文或与该论文直接相关的学术论文或成果时，署名单位仍然为青岛大学。本学位论文属于：保密口，在年解密后适用于本声明。不保密影(请在以上方框内打“~／”)论文作者签名；孑b、南面日期t矿唧年妇7日导师签名；弋义丧^一日期：舛石月汐目、，／(本声明的版权归青岛大学所有，未经许可，任何单位及任何个人不得擅自使用)青岛大学硬士学位论文Chapter1IntroductionTheH》theoryisinitiallyestabHshedin1940sbymathematicianssuch船G．H．H

3、ardy,J．E．LittlewoodandM．Reisz．TheearlyworkofthemWal$mainlyfocusedonthepropertiesofsomesubstantialfunctionsinI-IV．PeoplehadbecomemoreinterestedintheH’spacessincefunctionalanalysisdevelopedmorewaystostudyfunctionalspaces．TheTheoryofI-Ip8pace8，whichwaswrittenbyPe

4、terL．Durenin1970，notonlysummedupthemostimportantresultsoftheearlierwork，butalsorecordedthelatestdevelopmentsof日ptheoryatthattime．∥．ismuchmorefamiliartonsbecauseofitsgreatcontributiontodifferentialequations，probabilitytheory,andfunctionaltheory,Itshouldbenotedt

5、hattheH’spaceandtheLpspacehaveacloserelationshipwitheachother，since∥isisomorphictoLPwhenp21．Asaresult，weusuallyfocusonthecaseP<1whenwestudythespace日9．Generallyspeaking，theHardyspaceisconstructedwithanalyticfunctionsofcomplexvaluesordistributedfunctionsofrealva

6、lues．How-ever，sincethetheoryoftheHardyspacesandthefunctionalanalysishaveacloserelationshipwitheachother，weshallextendtherangeofthevalueoffunctionsinHpontotheBanachspace．whichisoneofthemostimportantspacesoffunctionaltheory．Thenitwouldbeconvenienttosubstitutethe

7、Banach-valuedfunctionsfortheC-valuedfunctionsintheHardyspace．ThenewspaceshallbedenotedasBH’inthispaper．Inthe8aineway,correspondingtothepspaceweshalltoodefineanewspacegeneratedbyBanach·valuedfunctionsanddenoteitasBLp．Wbstatetherelativedefinitions舳follows．1Chapt

8、er1IntroductionDEFINITION1．1．1etXbeacomplexBanachspace，and△isaconnectedopenset，△∈C，and，isaX-valuedfunctiondefinedonA．Ifgivenany知∈△，thereexistsf'CA)∈xsuchthat概

9、I瞥卅圳l_o，where¨0isahor