Singular Integrals and Differentiability Properties of Functions

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Princeton University Press, 1970 - 287 páginas

Singular integrals are among the most interesting and important objects of study in analysis, one of the three main branches of mathematics. They deal with real and complex numbers and their functions. In this book, Princeton professor Elias Stein, a leading mathematical innovator as well as a gifted expositor, produced what has been called the most influential mathematics text in the last thirty-five years. One reason for its success as a text is its almost legendary presentation: Stein takes arcane material, previously understood only by specialists, and makes it accessible even to beginning graduate students. Readers have reflected that when you read this book, not only do you see that the greats of the past have done exciting work, but you also feel inspired that you can master the subject and contribute to it yourself.


Singular integrals were known to only a few specialists when Stein's book was first published. Over time, however, the book has inspired a whole generation of researchers to apply its methods to a broad range of problems in many disciplines, including engineering, biology, and finance.


Stein has received numerous awards for his research, including the Wolf Prize of Israel, the Steele Prize, and the National Medal of Science. He has published eight books with Princeton, including Real Analysis in 2005.

 

Índice

SOME FUNDAMENTAL NOTIONS OF REALVARIABLE THEORY
3
Behavior near general points of measurable sets
12
An interpolation theorem for
20
SINGULAR INTEGRALS
26
Singular integral operators which commute with dilations
38
Vectorvalued analogues
45
RIESZ TRANSFORMS POISSON INTEGRALS AND SPHERICAL
54
Poisson integrals and approximations to the identity
60
82
135
The spaces A of Lipschitz continuous functions α
141
The spaces A2 9
150
Further results
159
EXTENSIONS AND RESTRICTIONS
166
RETURN TO THE THEORY OF HARMONIC FUNCTIONS
196
86
226
DIFFERENTIATION OF FUNCTIONS
240

Higher Riesz transforms and spherical harmonics
68
THE LITTlewoodPaleY THEORY AND MULTIPLIERS
81
DIFFERENTIABILITY PROPERTIES IN TERMS OF FUNCTION SPACES
116
Bessel potentials
130

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