Format:
1 Online-Ressource (711 p)
ISBN:
9780691032160
Series Statement:
Princeton Mathematical Series v.43
Content:
Cover -- Title -- Copyright -- Dedication -- Contents -- PREFACE -- GUIDE TO THE READER -- PROLOGUE -- I. REAL-VARIABLE THEORY -- 1. Basic assumptions -- 2. Examples -- 3. Covering lemmas and the maximal function -- 4. Generalization of the Calderón-Zygmund decomposition -- 5. Singular integrals -- 6. Examples of the general theory -- 7. Appendix: Truncation of singular integrals -- 8. Further results -- II. MORE ABOUT MAXIMAL FUNCTIONS -- 1. Vector-valued maximal functions -- 2. Nontangential behavior and Carleson measures -- 3. Two applications
Content:
4. Singular approximations of the identity -- 5. Further results -- III. HARDY SPACES -- 1. Maximal characterization of H^P -- 2. Atomic decomposition for H^P -- 3. Singular integrals -- 4. Appendix: Relation with harmonic functions -- 5. Further results -- IV. H^1 AND BMO -- 1. The space of functions of bounded mean oscillation -- 2. The sharp function -- 3. An elementary approach and a dyadic version -- 4. Further properties of BMO -- 5. An interpolation theorem -- 6. Further results -- V. WEIGHTED INEQUALITIES -- 1. The class Ap
Content:
2. Two further characterizations of Ap -- 3. The main theorem about Ap -- 4. Weighted inequalities for singular integrals -- 5. Further properties of Ap weights -- 6. Further results -- VI. PSEUDO-DIFFERENTIAL AND SINGULAR INTEGRAL OPERATORS: FOURIER TRANSFORM -- 1. Pseudo-differential operators -- 2. An L^2 theorem -- 3. The symbolic calculus -- 4. Singular integral realization of pseudo-differential operators -- 5. Estimates in L^P, Sobolev, and Lipschitz spaces -- 6. Appendix: Compound symbols -- 7. Further results
Content:
VII. PSEUDO-DIFFERENTIAL AND SINGULAR INTEGRAL OPERATORS: ALMOST ORTHOGONALITY -- 1. Exotic and forbidden symbols -- 2. Almost orthogonality -- 3. L^2 theory of operators with Calderón-Zygmund kernels -- 4. Appendix: The Cauchy integral -- 5. Further results -- VIII. OSCILLATORY INTEGRALS OF THE FIRST KIND -- 1. Oscillatory integrals of the first kind, one variable -- 2. Oscillatory integrals of the first kind, several variables -- 3. Fourier transforms of measures supported on surfaces -- 4. Restriction of the Fourier transform -- 5. Further results
Content:
IX. OSCILLATORY INTEGRALS OF THE SECOND KIND -- 1. Oscillatory integrals related to the Fourier transform -- 2. Restriction theorems and Bochner-Riesz summability -- 3. Fourier integral operators: L^2 estimates -- 4. Fourier integral operators: L^P estimates -- 5. Appendix: Restriction theorems in two dimensions -- 6. Further results -- X. MAXIMAL OPERATORS: SOME EXAMPLES -- 1. The Besicovitch set -- 2. Maximal functions and counterexamples -- 3. Further results -- XI. MAXIMAL AVERAGES AND OSCILLATORY INTEGRALS
Content:
1. Maximal averages and square functions
Note:
Description based upon print version of record
Additional Edition:
9781400883929
Additional Edition:
Erscheint auch als Druck-Ausgabe Stein, Elias M Harmonic Analysis (PMS-43) : Real-Variable Methods, Orthogonality, and Oscillatory Integrals. (PMS-43) Princeton : Princeton University Press,c2016 9780691032160
Language:
English
Keywords:
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