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[德]陆 著 / 世界图书出版公司 / 2008-08 / 平装
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实Hp空间四讲
Thewholebookconsistsoffourchapters.ThebasictheoryofFefferman-SteinonrealHpspacesisbrieflyintroducedinChapter1.ThecontentsinChapter2involvetheatomicdecompositiontheoryandthemoleculardecompositiontheoryofrealHpspaces.Inaddition,thedualspacesofrealHpspaces,theinterpolationofoperatorsinHpspaces,andtheinterpolationofHpspacesarealsodiscussedinChapter2asaprerequisiteforChapters3and4.ThepropertiesofseveralbasicoperatorsinHpspaceswillbediscussedinChapter3indetail.Amongthem,somebasicresultsarecontributedbyChinesemathematicians,suchasthedecompositiontheoryofweakHpspacesanditsapplicationstothestudyonthesharpnessofsingularintegrals,anewmethodtodealwiththeellipticRieszmeansinHpspaces,andthetransferencetheoremofHpmultipliers,etc.ThelastchapterisdevotedtoapplicationsofrealHPspacestoapproximationtheory.ThematerialsinChapter4arefullycontributedbyChinesemathematicians.
PrefaceChapter1RealVariableTheoryofHp(R2)Spaces1DefinitionofHp(Rn)spaces2Non-tangentialmaximalfunctions3GrandmaximalfunctionsChapter2DecompositionStructureTheoryofHp(Rn)Spaces1Atom2DualspaceofH1(Rn)3Atomdecomposition4DualspaceofHp(Rn)5Interpolationofoperators6InterpolationsofHpspaces;weakHpspaces7Molecule;moleculedecomposition8ApplicationstotheboundednessofoperatorsChapter3ApplicationstoFourierAnalysis1Fouriertransform2TheFouriermultiplier3TheRieszpotentialoperators4Singularintegraloperators5TheBochner-Rieszmeans6TransferencetheoremsofHpmultipliersChpater4ApplicationstoApproximationTheory1Kfunctional2HPmultiplierandJackson-typeinequality3HpmultiplierandBernsteintypeinequality4ApproximationbyBochner-RieszmeansatcriticalindexReferences
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