包邮经典傅里叶分析-第2版

lpspacesandinterpolation 1.1lpandweaklp 1.2convolutionandapproximateidentifies 1.3interpolation 1.4lorentzspaces 2maximalfunctions,fouriertransform,anddistributions 2.1maximalfunctions 2.2theschwartzclassandthefouriertransform 2.3theclassoftempereddistributions 2.4moreaboutdistributionsandthefouriertransform 2.5convolutionoperatorsonlpspacesandmultipliers 2.6oscillatoryintegrals 3fourieranalysisonthetorus 3.1fouriercoefficients 3.2decayoffouriercoefficients 3.3pointwiseconvergenceoffourierseries 3.4divergenceoffourierandbochner-rieszsummability 3.5theconjugatefunctionandconvergenceinnorm 3.6multipliers,transference,andalmosteverywhereconvergence .3.7lacunaryseries 4singularintegralsofconvolutiontype 4.1thehilberttransformandtheriesztransforms 4.2homogeneoussingularintegralsandthemethodofrotations. 4.3thecalder6n-zygmunddecompositionandsingularintegrals4.4sufficientconditionsfor/fboundedness4.5vector-valuedinequalities4.6vector-valuedsingularintegrals5littlewood-paleytheoryandmultipliers5.1littlewood-paleytheory5.2twomultipliertheorems5.3applicationsoflittlewood-paleytheory5.4thehaarsystem,conditionalexpectation,andmartingales5.5thesphericalmaximalfunction5.6waveletsagammaandbetafunctionsa.1ausefulformulaa.2definitionsoff(z)andb(z,w)a.3volumeoftheunitballandsurfaceoftheunitspherea.4computationofintegralsusinggammafunctionsa.5meromorphicextensionsofb(z,w)andf(z)a.6asymptoticsofγ(x)asx→∞.a.7euler'slimitformulaforthegammafunctiona.8reflectionandduplicationformulasforthegammafunctionbbesselfunctionsb.1definitionb.2somebasicpropertiesb.3aninterestingidentityb.4thefouriertransformofsurfacemeasureonsn-1b.5thefouriertransformofaradialfunctiononrnb.6besselfunctionsofsmallargumentsb.7besselfunctionsoflargeargumentsb.8asymptoticsofbesselfunctionscrademacherfunctionsc.1definitionoftherademacherfunctionsc.2khintchine'sinequalitiesc.3derivationofkhintchine'sinequalitiesc.4khintchine'sinequalitiesforweaktypespacesc.5extensiontoseveralvariablesdsphericalcoordinatesd.1sphericalcoordinateformulad.2ausefulchangeofvariablesformulad.3computationofanintegraloverthesphered.4thecomputationofanotherintegraloverthesphered.5integrationoverageneralsurfaced.6thestereographicprojectionesometrigonometricidentitiesandinequalitiesfsummationbypartsgbasicfunctionalanalysishtheminimaxlemmatheschurlemma1.1theclassicalschurlemma1.2schur'slenunaforpositiveoperators1.3anexamplejthewhitneydecompositionofopensetsinrnksmoothnessandvauinhingmomentsk.1thecaseofnocancellationk.2thecaseofcancellationk.3thecaseofthreefactorsglossaryreferencesindex