出版说明
序
Preface
Chapter1LpSpaceandInterpolation
1.1LpandWeekLp
1.2ConvolutionandApproximateIdentities
1.3Interpolation
1.4LorentzSpace
Chapter2MaximalFunctions,FourierTransform,andDistributions
2.1MaximalFunctions
2.2TheSchwartzClassandtheFourierTransform
2.3TheClassofTemperedDistributions
2.4MoreaboutDistributionsandtheFourierTransform
2.5ConvolutionOperatorsonLpSpacesandMultipliers
Chapter3FourierAnalysisontheTorus
3.1FourierCoefficients
3.2DecayofFourierCoefficients
3.3PointwiseConvergenceofFourierSeries
3.4DivergenceofFourierSeriesandBochner-RieszSummablility
3.5TheConjugateFunctionandConvergenceinNorm
3.6Multipliers,Transference,andAlmostEverywhereConvergence
3.7LacunarySeries
Chapter4SingularIntegralsofConvolutionType
4.1TheHibertTransformandtheRieszTransforms
4.2HomogeneousSingularIntegralsandtheMethodofRotations
4.3TheCalderon-zygmundDecompositionandSingularIntegrals
4.4SufficientConditionsforLpBoundedness
4.5Vector-ValuedInequalities
4.6Vector-ValuedSingularIntegrals
Chapter5Littlewood-paleyTheoryandMultipliers
5.1Littlewood-paleyTheory
5.2TwoMultiplierTherrems
5.3ApplicationsofLittlewood-paleyTheory
5.4TheHaarSystem,ConditionalExpectation,andMartingales
5.5TheSphericalMaximalFunction
5.6Wavelets
Chapter6SmoothnessandFunctionSpaces
6.1RieszPotentials,BesselPotentials,andFractionalIntegrals
6.2SobolevSpaces
6.3LipschitzSpaces
6.4HardySpaces
6.5Besov-LipschitzandTriebel-LizorkinSpaces
6.6AtomicDecomposition
6.7SingularIntegralsonFunctionSpaces
Chapter7BMOandCarlesonMeasures
7.1FunctionsofBoundedMeanOscillation
7.2DualityBetweenH1andCarlesonMeasures
7.3NontangentialMaximalFunctionsandCarlesonMeasures
……
Chapter8SingularIntegralsofNonconvolutionType
Chapter9WeightedIntequalities
Chapter10BoundednessandConvergenceofFourierIntegrals
AppendixAGammaandBetaFunctions
AppendixBBesselFunctions
AppendixCRademacherFunctions
AppendixDSphericalCoordinates
AppendixESomeTrigonometricIdentitiesandInequalities
AppendixFSummationbyParts
AppendixGBasicFunctionalAnalysis
AppendixHTheMinimaxLemma
AppendixITheSchurLemma
AppendixJTheWhitneyDecompositionofopensetsinRn
AppendixKSmoothnessandVanishingMoments
Bibliography
IndexofNotation
Index
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