UID:
almahu_9947367866602882
Format:
1 online resource (407 p.)
ISBN:
1-281-79724-3
,
9786611797249
,
0-08-087157-7
Series Statement:
Notas de matematica ; 75
Content:
Real variable methods in Fourier analysis
Note:
Description based upon print version of record.
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Front Cover; Real Variable Methods in Fourier Analysis; Copyright Page; TABLE OF CONTENTS; DEDICATION; PREFACE; CHAPTER 1. POINTWISE CONVERGENCE OF A SEQUENCE OF OPERATORS; 1.1. Finiteness a.e. and Continuity in measure of the maximal operator; 1.2. Continuity in measure at o e X of the maximal operator and a.e. convergence; CHAPTER 2. FINITENESS A.E. AND THE TYPE OF THE MAXIMAL OPERATOR; 2.1. A result of A. P. calderón on the partial sums of the fourier series of f e L2(T); 2.2. Commutativity of T* with mixing transformations. Positive operators. The theorem of Sawyer
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2.3. Commutativity of T* with mixing transformations. The theorem of Stein2.4. The theorem of Nikishin; CHAPTER 3. GENERAL TECHNIQUES FOR THE STUDY OF THE MAXIMAL OPERATOR; 3.1. Reduction to a dense subspace; 3.2. Covering and decomposition; 3.3. Kolmogorov condition and the weak type of an operator; 3.4. Interpolation; 3.5. Extrapolation; 3.6. Majorization; 3.7. Linearization; 3.8. Summation; CHAPTER 4. ESPECIAL TECHNIQUES FOR CONVOLUTION OPERATORS; 4.1. The type (1,1) of maximal convolution operators; 4.2. The type (p,p), p〉1, of maximal convolution operators
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CHAPTER 5. ESPECIAL TECHNIQUES FOR THE TYPE (2,2)5.1. Fourier transform; 5.2. Cotlar's lemma; 5.3. The method of rotation; CHAPTER 6. COVERINGS, THE HARDY-LITTLEWOOD MAXIMAL OPERATOR AND DIFFERENTIATION. SOME GENERAL THEOREMS; 6.1. Some notation; 6.2. Covering lemmas imply weak type properties of the maximal operator and differentiation; 6.3. From the maximal operator to covering properties; 6.4. Differentiation and the maximal operator; 6.5. Differentiation properties imply covering properties; 6.6. The halo problem; CHAPTER 7. THE BASIS OF INTERVALS
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7.1. The interval basis B2 does not have the Vitali property. It does not differentiate L17.2. Differentiation properties of B2. Weak type inequality for a basis which is the Cartesian product of another two; 7.3. The halo function of B2. Saks rarity theorem; 7.4. A theorem of Besicovitch on the possible values of the upper and lower derivatives with respect to B2; 7.5. A theorem of Marstrand and some generalizations; 7.6. A problem of Zygmund solved by Moriyón; 7.7. Covering properties of the basis of intervals . A theorem of Córdoba and R. Fefferman
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7.8. Another problem of Zygmund. Solution by CórdobaCHAPTER 8. THE BASIS OF RECTANGLES; 8.1. The Perron tree; 8.2. A lemma of Fefferman; 8.3. The Kakeya problem; 8.4. The Besicovitch set; 8.5. The Nikodym set; 8.6. Differentiation properties of some bases of rectangles; 8.7. Some results concerning bases of rectangles in lacunary directions; CHAPTER 9. THE GEOMETRY OF LINEARLY MEASURABLE SETS; 9.1. Linearly measurable sets; 9.2. Density. Regular and irregular sets; 9.3. Tangency properties; 9.4. Projection properties; 9.5. Sets of polar lines; 9.6. Some applications
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CHAPTER 10. APPROXIMATIONS OF THE IDENTITY
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English
Additional Edition:
ISBN 0-444-86124-6
Language:
English
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