奇异积分和函数的可微性

图书标准信息

• 作者 施泰恩（Stein E.M.） 著
• 出版社 世界图书出版公司
• 出版时间 2011-06
• 版次 1
• ISBN 9787510035135
• 定价 39.00元
• 装帧 平装
• 开本 24开
• 纸张 胶版纸
• 页数 287页
• 正文语种 英语

【内容简介】

ThisbookisanoutgrowthofacoursewhichIgaveatOrsayduringtheacademicyear1966.67MYpurposeinthoselectureswastopre-sentsomeoftherequiredbackgroundandatthesametimeclarifytheessentialunitythatexistsbetweenseveralrelatedareasofanalysis.Theseareasare：theexistenceandboundednessofsingularintegralop-erators；theboundarybehaviorofharmonicfunctions；anddifferentia-bilitypropertiesoffunctionsofseveralvariables.ASsuchthecommoncoreofthesetopicsmaybesaidtorepresentoneofthecentraldevelop-mentsinn.dimensionalFourieranalysisduringthelasttwentyyears，anditcanbeexpectedtohaveequalinfluenceinthefuture.Thesepos.

【作者简介】

作者：(美国)施泰恩(SteinE.M.)

【目录】

PREFACE
NOTATION
I．SOMEFUNDAMENTALNOTIONSOFREAL．VARIABLETHEORY
Themaximalfunction
Behaviorneargeneralpointsofmeasurablesets
DecompositionincubesofopensetsinR”
AninterpolationtheoremforL
Furtherresults

II．SINGULARINTEGRALS
ReviewofcertainaspectsofharmonicanalysisinR”
Singularintegrals：theheartofthematter
Singularintegrals：someextensionsandvariantsofthe
preceding
Singularintegraloperaterswhichcommutewithdilations
Vector．valuedanalogues
Furtherresults

III．RIESZTRANSFORMS，POLSSONINTEGRALS，ANDSPHERICAIHARMONICS
TheRiesztransforms
Poissonintegralsandapproximationstotheidentity
HigherRiesztransformsandsphericalharmonics
Furtherresults

IV．THELITTLEWOOD．PALEYTHEORYANDMULTIPLIERS
TheLittlewood-Paleyg-function
Thefunctiong
Multipliers（firstversion）
Applicationofthepartialsumsoperators
Thedyadicdecomposition
TheMarcinkiewiczmultipliertheorem
Furtherresults

V．DIFFERENTIABlLITYPROPERTIESINTERMSOFFUNCTIONSPACES
Rieszpotentials
TheSobolevspaces
BesseIpotentials
ThespacesofLipschitzcontinuousfunctions
Thespaces
Furtherresults

VI．EXTENSIONSANDRESTRICTIONS
Decompositionofopensetsintocubes
ExtensiontheoremsofWhitneytype
Extensiontheoremforadomainwithminimallysmooth
boundary
Furtherresults

VII．RETURNTOTHETHEORYOFHARMONICFUNCTIONS
Non-tangentialconvergenceandFatou'Stheorem
Theareaintegral
ApplicationofthetheoryofH”spaces
Furtherresults

VIII．DIFFERENTIATIONOFFUNCTIONS
Severalqotionsofpointwisedifierentiability
Thesplittingoffunctions
Acharacterization0fdifrerentiability
Desymmetrizationprinciple
AnothercharacterizationofdifirerentiabiliW
Furtherresults
APPENDICES
SomeInequalities
TheMarcinkiewiczInterpolationTheorem
SomeElementaryPropertiesofHarmonicFunctions
InequalitiesforRademacherFunctions
BlBLl0GRAPHY
INDEX