Preface
CHAPTERⅠTheFourierTransform
1.ThebasicL1theoryoftheFouriertransform
2.TheL2theoryandthePlanchereltheorem
3.Theclassoftempereddistributions
4.Furtherresults
CHAPTERⅡBoundaryValuesofHarmonicFunctions
1.Basicpropertiesofharmonicfunctions
2.ThecharacterizationofPoissonintegrals
3.TheHardy-Littlewoodmaximalfunctionandnontangentialconvergenceofharmonicfunctions
4.Subharmonicfunctionsandmajorizationbyharmonicfunctions
5.Furtherresults
CHAPTERⅢTheTheoryofHpSpacesonTubes
1.Introductoryremarks
2.TheH2theory
3.Tubesovercones
4.ThePaley-Wienertheorem
5.TheHptheory
6.Furtherresults
CHAPTERⅣSymmetryPropertiesoftheFourierTransform
1.DecompositionofL2(Ez)intosub,pacesinvariantundertheFouriertransform
2.Sphericalharmonics
3.TheactionoftheFouriertransformonthespaces
4.Someapplications
5.Furtherresults
CHAPTERⅤInterpolationofOperators
1.TheM.RieszconvexitytheoremandinterpolationofoperatorsdefinedonLpspaces
2.TheMarcinkiewiczinterpolationtheorem
3.L(p,q)spaces
4.Interpolationofanalyticfamiliesofoperators
5.Furtherresults
CHAPTERⅥSingularIntegralsandSystemsofConjugateHarmonicFunctions
1.TheHilberttransform
2.Singularintegraloperatorswithoddkernels
3.Singularintegraloperatorswithevenkernels
4.Hpspacesofconjugateharmonicfunctions
5.Furtherresults
CHAPTERⅦMultipleFourierSeries
1.Elementaryproperties
2.ThePoissonsummationformula
3.Multipliertransformations
4.Summabilitybelowthecriticalindex(negativeresults)
5.Summabilitybelowthecriticalindex
6.Furtherresults
Bibliography
Index