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Analysis and Geometry on Groups (Cambridge Tracts in Mathematics)-Varopoulos saloff-coste coulhon .pdf

Analysis and Geometry on Groups (Cambridge Tracts in Mathematics)-Varopoulos saloff-coste coulhon .pdf

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时间：2019-03-10

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1、CAMBRIDGETRACTSINMATHEMATICSGeneralEditorsB.BOLLOBAS,P.SARNAK,C.T.C.WALL100AnalysisandGeometryonGroupsAnalysisandGeometryonGroupsN.Th.VaropoulosL.Saloff-CosteT.CoulhonUniversitedeParis,VICAMBRIDGEUNIVERSITYPRESSCAMBRIDGEUNIVERSITYPRESSCambridge,NewYork,Melbourne,Madrid,CapeTown,Singapore,SaoPa

2、ulo,DelhiCambridgeUniversityPressTheEdinburghBuilding,CambridgeCB28RU,UKPublishedintheUnitedStatesofAmericabyCambridgeUniversityPress,NewYorkwww.cambridge.orgInformationonthistitle:www.cambridge.org/9780521353823©CambridgeUniversityPress1992Thispublicationisincopyright.Subjecttostatutoryexcept

3、ionandtotheprovisionsofrelevantcollectivelicensingagreements,noreproductionofanypartmaytakeplacewithoutthewrittenpermissionofCambridgeUniversityPress.Firstpublished1992Thisdigitallyprintedversion2008AcataloguerecordforthispublicationisavailablefromtheBritishLibraryISBN978-0-521-35382-3hardback

4、ISBN978-0-521-08801-5paperbackCONTENTSPrefaceviiForewordixIIntroduction11SobolevinequalitiesinR'12SobolevinequalitiesandtheheatequationonLiegroups33Harnack'sprinciple54Aguidetothisbook6IIDimensionalinequalitiesforsemigroupsofoperatorsontheLPspaces81Introduction,notation82Hardy-Littlewood-Sobol

5、evtheory93ConversestotheHardy-Littlewood-Sobolevtheory124Localizations175Symmetricsubmarkoviansemigroups20ReferencesandComments25IIISystemsofvectorfieldssatisfyingHormander'scondition261Hormander'sconditionandhypoellipticity26Uniformitymatters272Harnackinequalities28Uniformitymatters323Theexpo

6、nentialmap344Carnot-Caratheodorydistances39ReferencesandComments41IVTheheatkernelonnilpotentLiegroups421SomeremarkablepropertiesofnilpotentLiegroups422Examples433HarnackinequalitiesfornilpotentLiegroups454Estimatesoftheheatkernel485Estimatesofthevolume506Sobolev'stheorem557Sobolevinequalities5

7、6ReferencesandComments61VLocaltheoryforsumsofsquaresofvectorfields631Estimatesofthevolume632ProofoftheKeyLemma653LocalscalingoftheHarnackinequality67vi4ThecaseofunimodularLiegroups695Thegeneralcase70ReferencesandComments72VIConvolutionp

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