Princeton University Library Catalog

Singular integrals and differentiability properties of functions / [by] Elias M. Stein.

Author:
Stein, Elias M., 1931- [Browse]
Format:
Book
Language:
English
Published/​Created:
Princeton, N.J., Princeton University Press, 1970.
Description:
1 online resource (xiv, 287 pages) : illustrations.
Series:
Notes:
An outgrowth of the author's Intégrales singulières et fonctions différentiables de plusieurs variables.
Bibliographic references:
Includes bibliographical references (pages 279-287).
Source of description:
Print version record.
Contents:
  • Cover; Title; Copyright; Dedication; Contents; PREFACE ; NOTATION ; I. SOME FUNDAMENTAL NOTIONS OF REAL-VARIABLE THEORY ; 1. The maximal function ; 2. Behavior near general points of measurable sets ; 3. Decomposition in cubes of open sets in R^n; 4. An interpolation theorem for L^p; 5. Further results ; II. SINGULAR INTEGRALS.
  • 1. Review of certain aspects of harmonic analysis in R^n2. Singular integrals: the heart of the matter ; 3. Singular integrals: some extensions and variants of the preceding ; 4. Singular integral operators which commute with dilations ; 5. Vector-valued analogues ; 6. Further results.
  • III. RIESZ TRANSFORMS, POISSON INTEGRALS, AND SPHERICAL HARMONICS 1. The Riesz transforms ; 2. Poisson integrals and approximations to the identity ; 3. Higher Riesz transforms and spherical harmonics ; 4. Further results ; IV. THE LITTLEWOOD-PALEY THEORY AND MULTIPLIERS; 1. The Littlewood-Paley g-function.
  • 2. The function3. Multipliers (first version) ; 4. Application of the partial sums operators ; 5. The dyadic decomposition ; 6. The Marcinkiewicz multiplier theorem ; 7. Further results ; V. DIFFERENTIABILITY PROPERTIES IN TERMS OF FUNCTION SPACES; 1. Riesz potentials ; 2. The Sobolev spaces; 3. Bessel potentials.
  • 4. The spaces Λa of Lipschitz continuous functions5. The spaces; 6. Further results ; VI. EXTENSIONS AND RESTRICTIONS; 1. Decomposition of open sets into cubes ; 2. Extension theorems of Whitney type ; 3. Extension theorem for a domain with minimally smooth boundary ; 4. Further results ; VII. RETURN TO THE THEORY OF HARMONIC FUNCTIONS.
Subject(s):
ISBN:
  • 9781400883882 (electronic bk.)
  • 1400883881 (electronic bk.)
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