Real-variable Methods in Harmonic Analysis
Published on 6. November 1986
461 pages
978-0-08-087442-5 (ISBN)
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Real-variable Methods in Harmonic Analysis
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Alberto Torchinsky
Real Variable Methods in Harmonic Analysis
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01/1986
Academic Press
€136.18
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Content
- Front Cover
- Real-Variable Methods in Harmonic Analysis
- Copyright Page
- Contents
- Preface
- Chapter I. Fourier Series
- 1. Fourier Series of Functions
- 2. Fourier Series of Continuous Functions
- 3. Elementary Properties of Fourier Series
- 4. Fourier Series of Functionals
- 5. Notes
- Further Results and Problems
- Chapter II. Cesàro Summability
- 1. (C, 1) Summability
- 2. Fejbér's Kernel
- 3. Characterization of Fourier Series of Functions and Measures
- 4. A.E. Convergence of (C, 1) Means of Summable Functions
- 5 . Notes
- Further Results and Problems
- Chapter III. Norm Convergence of Fourier Series
- 1. The Case L2( T)
- Hilbert Space
- 2. Norm Convergence in Lp(T), 1 & p& 00
- 3. The Conjugate Mapping
- 4. More on Integrable Functions
- 5 . Integral Representation of the Conjugate Operator
- 6. The Truncated Hilbert Transform
- 7. Notes
- Further Results and Problems
- Chapter IV. The Basic Principles
- 1. The Calderón-Zygmund Interval Decomposition
- 2. The Hardy-Littlewood Maximal Function
- 3. The Calderón-Zygmund Decomposition
- 4. The Marcinkiewicz Interpolation Theorem
- 5 . Extrapolation and the Zygmund L In L Class
- 6. The Banach Continuity Principle and a.e. Convergence
- 7. Notes
- Further Results and Problems
- Chapter V. The Hilbert Transform and Multipliers
- 1. Existence of the Hilbert Transform of Integrable Functions
- 2. The Hilbert Transform in LP(T), 1&= p & 00
- 3. Limiting Results
- 4. Multipliers
- 5. Notes
- Further Results and Problems
- Chapter VI. Paley's Theorem and Fractional Integration
- 1. Paley's Theorem
- 2. Fractional Integration
- 3. Multipliers
- 4. Notes
- Further Results and Problems
- Chapter VII. Harmonic and Subharmonic Functions
- 1. Abel Summability, Nontangential Convergence
- 2. The Poisson and Conjugate Poisson Kernels
- 3. Harmonic Functions
- 4. Further Properties of Harmonic Functions and Subharmonic Functions
- 5 . Harnack's and Mean Value Inequalities
- 6. Notes
- Further Results and Problems
- Chapter VIII. Oscillation of Functions
- 1. Mean Oscillation of Functions
- 2. The Maximal Operator and BMO
- 3. The Conjugate of Bounded and BMO Functions
- 4. Wk-Lp and Kf. Interpolation
- 5 . Lipschitz and Morrey Spaces
- 6. Notes
- Further Results and Problems
- Chapter IX. Ap Weights
- 1. The Hardy-Littlewood Maximal Theorem for Regular Measures
- 2. Ap Weights and the Hardy-Littlewood Maximal Function
- 3. A1 Weights
- 4. Ap Weights, p & 1
- 5. Factorization of Ap Weights
- 6. Ap and BMO
- 7. An Extrapolation Result
- 8. Notes
- Further Results and Problems
- Chapter X. More about Rn
- 1. Distributions. Fourier Transforms
- 2. Translation Invariant Operators. Multipliers
- 3. The Hilbert and Riesz Transforms
- 4. Sobolev and Poincaré Inequalities
- Chapter XI. Calderón-Zygmund Singular Integral Operators
- 1. The Bendek-Calderón-Panzone Principle
- 2 . A Theorem of Zó
- 3. Convolution Operators
- 4. Cotlar's Lemma
- 5. Calderón-Zygmund Singular Integral Operators
- 6. Maximal Calderón-Zygmund Singular Integral Operators
- 7. Singular Integral Operators in L00(Rn)
- 8. Notes
- Further Results and Problems
- Chapter XII. The Littlewood-Paley Theory
- 1. Vector-Valued Inequalities
- 2. Vector-Valued Singular Integral Operators
- 3. The Littlewood-Paley g Function
- 4. The Lusin Area Function and the Littlewood-Paley g*? Function
- 5. Hörmander's Multiplier Theorem
- 6. Notes
- Further Results and Problems
- Chapter XIII. The Good ?, Principle
- 1 . Good ? Inequalities
- 2. Weighted Norm Inequalities for Maximal CZ Singular Integral Operators
- 3. Weighted Weak-Type (1,1) Estimates for CZ Singular Integral Operators
- 4. Notes
- Further Results and Problems
- Chapter XIV. Hardy Spaces of Several Real Variables
- 1. Atomic Decomposition
- 2. Maximal Function Characterization of Hardy Spaces
- 3. Systems of Conjugate Functions
- 4. Multipliers
- 5. Interpolation
- 6. Notes
- Further Results and Problems
- Chapter XV Carleson Measures
- 1. Carleson Measures
- 2. Duals of Hardy Spaces
- 3. Tent Spaces
- 4. Notes
- Further Results and Problems
- Chapter XVI Cauchy Integrals on Lipschitz Curves
- 1 . Cauchy Integrals on Lipschitz Curves
- 2. Related Operators
- 3. The T1 Theorem
- 4. Notes
- Further Results and Problems
- Chapter XVII Boundary Value Problems on C1-Domains
- 1. The Double and Single Layer Potentials on a C1-Domain
- 2. The Dirichlet and Neumann Problems
- 3. Notes
- Bibliography
- Index
