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GTM 250 graduate texts in mathematics 研究生数学丛书
[美]格拉法克斯(Grafakos L.) 著 / 世界图书出版公司 / 2011-01 / 平装
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数学研究生教材:现代傅里叶分析(英文)(第2版)(影印版)
ThegreatresponsetothepublicationofthebookClassicalandModernFourierAnalysishasbeenverygratifying.IamdelightedthatSpringerhasofferedtopublishthesecondeditionofthisbookintwovolumes:ClassicalFourierAnalysis,2ndEdition,andModernFourierAnalysis,2ndEdition.
ThesevolumesaremainlyaddressedtograduatestudentswhowishtostudyFourieranalysis.Thissecondvolumeisintendedtoserveasatextforasecond-semestercourseinthesubject.Itisdesignedtobeacontinuationofthefirstvolume.Chapters1-5inthefirstvolumecontainLebesguespaces,Lorentzspacesandinterpolation,maximalfunctions,Fouriertransformsanddistributions,anintroductiontoFourieranalysisonthen-torus,singularintegralsofconvolutiontype,andLittlewood-Paleytheory.
6SmoothnessandFunctionSpaces6.1RieszandBesselPotentials,FractionalIntegrals6.1.1RieszPotentials6.1.2BesselPotentialsExercises6.2SobolevSpaces6.2.1DefinitionandBasicPropertiesofGeneralSobolevSpaces6.2.2Littlewood-PaleyCharacterizationofInhomogeneousSobolevSpaces6.2.3Littlewood-PaleyCharacterizationofHomogeneousSobolevSpacesExercises6.3LipschitzSpaces6.3.1IntroductiontoLipschitzSpaces6.3.2Littlewood-PaleyCharacterizationofHomogeneousLipschitzSpaces6.3.3Littlewood-PaleyCharacterizationofInhomogeneousLipschitzSpacesExercises6.4HardySpaces6.4.1DefinitionofHardySpaces6.4.2QuasinormEquivalenceofSeveralMaximalFunctions6.4.3ConsequencesoftheCharacterizationsofHardySpaces6.4.4Vector-ValuedHpandItsCharacterizations6.4.5SingularIntegralsonHardySpaces6.4.6TheLittlewood-PaleyCharacterizationofHardySpacesExercises6.5Besov-LipschitzandTriebel-LizorkinSpaces6.5.1IntroductionofFunctionSpaces6.5.2EquivalenceofDefinitionsExercises……7BMOandCarlesonMeasures8SingularIntegralsofNonconvolutionType9WeightedInequalities10BoundednessandConvergenceofFourierIntegrals11Time-FrequencyAnalysisandtheCarleson-HuntTheoremGlossaryReferencesIndex
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