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| 內容簡介： |
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《奇异积分和函数的可微性(英文)(影印版)》内容简介：This book is an outgrowth of a course which I gave at Orsay duringthe academic year 1 966.67 MY purpose in those lectures was to pre-sent some of the required background and at the same time clarify theessential unity that exists between several related areas of analysis.These areas are：the existence and boundedness of singular integral op-erators；the boundary behavior of harmonic functions；and differentia-bility properties of functions of several variables.AS such the commoncore of these topics may be said to represent one of the central develop-ments in n.dimensional Fourier analysis during the last twenty years，and it can be expected to have equal influence in the future.These pos.
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| 目錄：
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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
Multipliersfirst 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
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