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1、第31卷第4期黑龍江大學(xué)自然科學(xué)學(xué)報(bào)Vol_31No．42014年8月JOURNALOFNATURALSCIENCEOFHEILONGJIANGUNIVERSITYAugust，2014DOI：10．13482／j．issnl001—7011．2014．01．241ThetwoweightedPoincar~norminequalitiesforthecompositionofGreenoperatorandhomotopyoperatorLIHua—can，XINGYu—ming，LIQUB—fang(1．SchoolofScience，JiangxiUnivers

2、ityofScienceandTechnology，Ganzhou341000，China；2．DepartmentofMathe‘matics，HarbinInstituteofTechnology，Harbin150001，China；3．DepartmentofMathematics，GanzhouTeachers’College，Ganzhou341000，China)Abstract：BasedontheresultsoftheLpboundednessofGreen’Soperatorandtheimbeddingine-qualityactingondi

3、fferentialforms，thePoincar6inequalitiesforthecompositionofGreen’SoperatorGandtheHomotopyoperatorTontheboundeddomainareproven．Thereby．thePoinear6一typenormes。timationforthecompositionofGandTactedontheconjugateA—harmonictensorsisachievedbyselectingu=d口．Atlast，byusingtheHtilderinequlityandt

4、hepropertyoftheA，(A，Q)-weight，theA，(A，Q)一twoweightedPoincar~integralinequalitiesaregiven．Keywords：norIninequalities；theHomotopyoperator；conjugateA—harmonictensors；A(A，Q)一twoweightsCLCnumber：O175．2Documentcode：AArticleID：1001—7011(2014)04一O484一O6關(guān)于格林算子和同倫算子的復(fù)合算子的雙權(quán)Ponincar6范數(shù)不等式李華燦，邢宇明，李

5、群芳(1．江西理工大學(xué)理學(xué)院，贛州341000；2．哈爾濱工業(yè)大學(xué)數(shù)學(xué)系，哈爾濱150001；3．贛州師范高等專(zhuān)科學(xué)校數(shù)學(xué)系，贛州341000)摘要：基于格林算子的Lp有界性和微分形式的嵌入不等式，證明有界域上關(guān)于格林算子和同倫算子的復(fù)合算子的Poincar6不等式；通過(guò)令U=d，得到作用于共軛A一調(diào)和張量的復(fù)合算子T。G的Poincar6一型范數(shù)估計(jì)。借助于HOlder不等式和A(A，Q)一權(quán)性質(zhì)的巧妙結(jié)合，給出A(A，n)一雙權(quán)的Poincar~一型積分不等式。關(guān)鍵詞：范數(shù)不等式；同倫算子；共軛A一調(diào)和張量；A，(A，)一雙權(quán)Receiveddate：2013一O

6、4—26Foundationitem：SupposedbytheYouthFoundationofJiangxiProvincialEducationDepartment(GJJ13376)；theFoundationoftheJiangxiUni—versityofScienceandTechnology(jxxj12073)Biography：Mr．LIHua—can(1985一)，lecturer，M．S．，interestedin：harmonicanalysis，E—mail：hua03010217@126．cornCitethis：LIHua—can，XI

7、NGYu—ming，LIQun-fang．ThetwoweightedPoinear~norminequalitiesforthecompositionofGreenoperatorandhomotoPYoperator[J]．JournalofNaturalScienceofHeilongjiangUniversity，2014，31(4)：484—489．第4期李華燦等：關(guān)于格林算子和同倫算子的復(fù)合算子的雙權(quán)Ponincar~范數(shù)不等式·485·0IntroductionTheA—harmonicequationswhichbelongtothe