內容簡介
《奇異積分和函式的可微性(英文)(影印版)》內容簡介：ThisbookisanoutgrowthofacoursewhichIgaveatOrsayduringtheacademicyear1966.67MYpurposeinthoselectureswastopre-sentsomeoftherequiredbackgroundandatthesametimeclarifytheessentialunitythatexistsbetweenseveralrelatedareasofanalysis.Theseareasare：theexistenceandboundednessofsingularintegralop-erators；theboundarybehaviorofharmonicfunctions；anddifferentia-bilitypropertiesoffunctionsofseveralvariables.ASsuchthecommoncoreofthesetopicsmaybesaidtorepresentoneofthecentraldevelop-mentsinn.dimensionalFourieranalysisduringthelasttwentyyears，anditcanbeexpectedtohaveequalinfluenceinthefuture.Thesepos.
目錄
PREFACE
NOTATION
I．SOME FUNDAMENTAL NOTIONS OF REAL．VARIABLE THEORY
The maximal function
Behavior near general points of measurable sets
Decomposition in cubes of open sets in R”
An interpolation theorem for L
Further results
II．SINGULAR INTEGRALS
Review of certain aspects of harmonic analysis in R”
Singular integrals：the heart of the matter
Singular integrals：some extensions and variants of the
preceding
Singular integral operaters which commute with dilations
Vector．valued analogues
Further results
III．RIESZ TRANSFORMS，POLSSON INTEGRALS，AND SPHERICAI HARMONICS
The Riesz transforms
Poisson integrals and approximations to the identity
Higher Riesz transforms and spherical harmonics
Further results
IV．THE LITTLEWOOD．PALEY THEORY AND MULTIPLIERS
The Littlewood-Paley g-function
The functiong
Multipliers(first version)
Application of the partial sums operators
The dyadic decomposition
The Marcinkiewicz multiplier theorem
Further results
V．DIFFERENTIABlLITY PROPERTIES IN TERMS OF FUNCTION SPACES
Riesz potentials
The Sobolev spaces
BesseI potentials
The spaces of Lipschitz continuous functions
The spaces
Further results
VI．EXTENSIONS AND RESTRICTIONS
Decomposition of open sets into cubes
Extension theorems of Whitney type
Extension theorem for a domain with minimally smooth
boundary
Further results
VII．RETURN TO THE THEORY OF HARMONIC FUNCTIONS
Non-tangential convergence and Fatou'S theorem
The area integral
Application of the theory of H”spaces
Further results
VIII．DIFFERENTIATION OF FUNCTIONS
Several qotions of pointwise difierentiability
The splitting of functions
A characterization 0f difrerentiability
Desymmetrization principle
Another characterization of difirerentiabiliW
Further results
APPENDICES
Some Inequalities
The Marcinkiewicz Interpolation Theorem
Some Elementary Properties of Harmonic Functions
Inequalities for Rademacher Functions
BlBLl0GRAPHY
INDEX
