Cargando…
Singular integrals and differentiability properties of functions /
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 gifte...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton, N.J. :
Princeton University Press,
1970.
|
| Colección: | Princeton mathematical series ;
30. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- 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.