加权极大算子bmo有界性

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1、©aÒ0174Æ“è10373—?ÆÒ11011071103分类号：学校代码：10373密级：学号：硕士学位论文(20133)题目：K8µ4ŒŽfBMOk.5论文作者：Ø©ŠöµÒwA指导教师：•专业名称：“µ&t;’研究方向：¶¡µÄ:êÆïÄ••µNÚ©Û•“‰ŒÆïÄ)?˜ncÊ淮北师范大学研究生处二○一二年五月4ŒŽfBMOk.5Á‡:Hardy-Littlewood4ŒŽfÚÛÉÈ©Žf´lebesgue˜mk.,4ŒŽf3OÛÉÈ©ž•åX•‡Š^,Ïdïļê,Hardy-Littlewood4ŒŽf¼êت¿Â•Œ.Hardy-

2、Littlewood4Œ¼ê´NÚ©ÛD–y“©Û¥ïļꘇ•‡óä,ÓžHary-Littlewood4ŒŽf•´NÚ©Û¥A‡²;Žfƒ˜.©ÏLCalderon-Zygmund©)½n!Hardy-littlewood4ŒŽf±9ÛÉÈ©Žfƒ'nØ5?Ø4ŒŽfBMOk.5"©Äk‰ÑHardy-littlewoodŽf½ÂÚÙ÷v˜{ü5Ÿ¶Ùg§qÚk.²þ˜m½Â†5Ÿ¶•§²Lí2ѧ÷vAp¼ê!(x)â´k.§Óž••k¼ê!(x)÷vAp^‡žÿ§Øªâ¤á"k.²þ˜m=•BMO˜m,Ù†E©Û!‡©•

3、§!VÇØ+•þk—ƒ'X,´y“©Û¥›©•‡ïÄé–ƒ˜.'…c:BMO˜m;¼ê;Ap^‡;Hardy-Littlewood4ŒŽf;IWeightedmaximaloperatorBMOboundedAbstract:Hardy-LittlewoodmaximaloperatorandsingularintegraloperatorsonLebesguespaceisbounded,andthemaximaloperatorintheestimationofsingu-larintegralalsoplaysanimportantrole,sothestudyofwei

4、ghtfunction,signicanceweightednorminequalitiesofHardy-Littlewoodmaximaloperatorfunctions.Hardy-Littlewoodmaximalfunctionisthefunctionoftheharmonicanalysisandanimpor-tantofthemodernanalysis.Atthesametime,operatorofHary-Littlewoodmaximalisoneofreconcileseveraloperatorinclassicalanalysis.Thispassag

5、ebasedCalderon-ZygmunddecompositiontheoremofHardy-littletheory,woodmaximaloperatorandsingularintegraloperatorsonweightedBMOboundednessofthemaximaloperator.ThispaperrstgivesthedenitionofHardy-littlewoodoperatoranditssatisfyingsomesimpleproperties;secondly,introducesthedenitionandnaturemeanoscilla

6、tionspace;nally,afterthepromotionofdraw,meettheApweightfunctionlomega(x)isbounded,andonlytheweightfunctionlomega(x)whenmeetApconditions,weightednorminequalitiesisestablished.BoundedmeanoscillationspaceisBMOspace,andthecomplexanalysis,partialdierentialequations,probabilitytheoryandothereldsareclo

7、selyrelated,isoneoftheimportantresearchobjectinmodernanalysis.Keywords:BMOspace;weightingfunction;Apcondition;Hardy-Littlewoodmaximaloperator;interpolationtheoremII8¹Á‡IAbstractII1˜ÙÚó9ý•£11.1Hardy-Littlewood4Œ¼ê...........