导考网短评: 《傅里叶分析(英文版)》讲述的是由Calderon和Zygmund引进的傅里叶分析的实变量方法。这本教材源自马德里自治大学的一门研究生课,并吸取了JoseLuisRubiodeFrancia在同一所大学授课的讲义内容。
§9.TheconvergenceandsummabilityofFourierintegrals§10.NotesandfurtherresultsChapter2.TheHardy-LittlewoodMaximalFunction§1.Approximationsoftheidentity§2.Weak-typeinequalitiesandalmosteverywhereconvergence§3.TheMarcinkiewiczinterpolationtheorem§4.TheHardy-Littlewoodmaximalfunction§5.Thedyadicmaximalfunction§6.Theweak(1,1)inequalityforthemaximalfunction§7.Aweightednorminequality§8.NotesandfurtherresultsChapter3.TheHilbertTransform§1.TheconjugatePoissonkernel§2.Theprincipalvalueof1/x§3.ThetheoremsofM.RieszandKolmogorov§4.Truncatedintegralsandpointwiseconvergence§5.Multipliers§6.NotesandfurtherresultsChapter4.SingularIntegrals(I)§1.Definitionandexamples§2.TheFouriertransformofthekernel§3.Themethodofrotations§4.Singularintegralswithevenkernel§5.Anoperatoralgebra§6.Singularintegralswithvariablekernel§7.NotesandfurtherresultsChapter5.SingularIntegrals(II)§1.TheCalderon-Zygmundtheorem§2.Truncatedintegralsandtheprincipalvalue§3.GeneralizedCalderon-Zygmundoperators§4.CalderSn-Zygmundsingularintegrals§5.Avector-valuedextension§6.NotesandfurtherresultsChapter6.H1andBMO§1.ThespaceatomicH1§2.ThespaceBMO§3.Aninterpolationresult§4.TheJohn-Nirenberginequality§5.NotesandfurtherresultsChapter7.WeightedInequalities§1.TheApcondition§2.Strong-typeinequalitieswithweights§3.A1weightsandanextrapolationtheorem§4.Weightedinequalitiesforsingularintegrals§5.NotesandfurtherresultsChapter8.Littlewood-PaleyTheoryandMultipliers§1.Somevector-valuedinequalities§2.Littlewood-Paleytheory§3.TheHSrmandermultipliertheorem§4.TheMarcinkiewiczmultipliertheorem§5.Bochner-Rieszmultipliers§6.Returntosingularintegrals§7.ThemaximalfunctionandtheHilberttransformalongaparabola§8.NotesandfurtherresultsChapter9.TheT1Theorem§1.Cotlar'slemma§2.Carlesonmeasures§3.StatementandapplicationsoftheT1theorem§4.ProofoftheT1theorem§5.NotesandfurtherresultsBibliographyIndex