关于格林算子和同伦算子的复合算子的双权Ponincaré范数不等式.pdf

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1、第31卷第4期黑龙江大学自然科学学报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关于格林算子和同伦算子的复合算子的双权Ponincar6范数不等式李华灿，邢宇明，李

5、群芳(1．江西理工大学理学院，赣州341000；2．哈尔滨工业大学数学系，哈尔滨150001；3．赣州师范高等专科学校数学系，赣州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，证明有界域上关于格林算子和同伦算子的复合算子的Poincar6不等式；通过令U=d，得到作用于共轭A一调和张量的复合算子T。G的Poincar6一型范数估计。借助于HOlder不等式和A(A，Q)一权性质的巧妙结合，给出A(A，n)一双权的Poincar~一型积分不等式。关键词：范数不等式；同伦算子；共轭A一调和张量；A，(A，)一双权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期李华灿等：关于格林算子和同伦算子的复合算子的双权Ponincar~范数不等式·485·0IntroductionTheA—harmonicequationswhichbelongtothe