Real-Variable Methods in Harmonic Analysis

ISBN-10: 0486435083
ISBN-13: 9780486435084
Edition: 2004
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Description: An exploration of the unity of several areas in harmonic analysis, this text emphasizes real-variable methods. Discusses classical Fourier series, summability, norm convergence, and conjugate function. Examines the Hardy-Littlewood maximal function,  More...

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Book details

List price: $26.95
Copyright year: 2004
Publisher: Dover Publications, Incorporated
Publication date: 4/9/2004
Binding: Paperback
Pages: 480
Size: 5.50" wide x 8.50" long x 1.25" tall
Weight: 1.034
Language: English

An exploration of the unity of several areas in harmonic analysis, this text emphasizes real-variable methods. Discusses classical Fourier series, summability, norm convergence, and conjugate function. Examines the Hardy-Littlewood maximal function, the Calderón-Zygmund decomposition, the Hilbert transform and properties of harmonic functions, the Littlewood-Paley theory, more. 1986 edition.

Preface
Fourier Series
Fourier Series of Functions
Fourier Series of Continuous Functions
Elementary Properties of Fourier Series
Fourier Series of Functionals
Notes; Further Results and Problems
Cesaro Summability
(C, 1) Summability
Fejer's Kernel
Characterization of Fourier Series of Functions and Measures
A.E. Convergence of (C, 1) Means of Summable Functions
Notes; Further Results and Problems
Norm Convergence of Fourier Series
The Case L[superscript 2](T); Hilbert Space
Norm Convergence in L[superscript p] (T), 1 [less than or equal] p [less than or equal] [infinity]
The Conjugate Mapping
More on Integrable Functions
Integral Representation of the Conjugate Operator
The Truncated Hilbert Transform
Notes; Further Results and Problems
The Basic Principles
The Calderon-Zygmund Interval Decomposition
The Hardy-Littlewood Maximal Function
The Calderon-Zygmund Decomposition
The Marcinkiewicz Interpolation Theorem
Extrapolation and the Zygmund L ln L Class
The Banach Continuity Principle and a. e. Convergence
Notes; Further Results and Problems
The Hilbert Transform and Multipliers
Existence of the Hilbert Transform of Integrable Functions
The Hilbert Transform in L[superscript p](T), 1 [less than or equal] p [less than sign] [infinity]
Limiting Results
Multipliers
Notes; Further Results and Problems
Paley's Theorem and Fractional Integration
Paley's Theorem
Fractional Integration
Multipliers
Notes; Further Results and Problems
Harmonic and Subharmonic Functions
Abel Summability, Nontangential Convergence
The Poisson and Conjugate Poisson Kernels
Harmonic Functions
Further Properties of Harmonic Functions and Subharmonic Functions
Harnack's and Mean Value Inequalities
Notes; Further Results and Problems
Oscillation of Functions
Mean Oscillation of Functions
The Maximal Operator and BMO
The Conjugate of Bounded and BMO Functions
Wk-L[superscript p] and K[subscript f]. Interpolation
Lipschitz and Morrey Spaces
Notes; Further Results and Problems
A[subscript p] Weights
The Hardy-Littlewood Maximal Theorem for Regular Measures
A[subscript p] Weights and the Hardy-Littlewood Maximal Function
A[subscript 1] Weights
A[subscript p] Weights, p [greater than sign] 1
Factorization of A[subscript p] Weights
A[subscript p] and BMO
An Extrapolation Result
Notes; Further Results and Problems
More about R[superscript n]
Distributions, Fourier Transforms
Translation Invariant Operators. Multipliers
The Hilbert and Riesz Transforms
Sobolev and Poincare Inequalities
Calderon-Zygmund Singular Integral Operators
The Benedek-Calderon-Panzone Principle
A Theorem of Zo
Convolution Operators
Cotlar's Lemma
Calderon-Zygmund Singular Integral Operators
Maximal Calderon-Zygmund Singular Integral Operators
Singular Integral Operators in L[superscript infinity] (R[superscript n])
Notes; Further Results and Problems
The Littlewood-Paley Theory
Vector-Valued Inequalities
Vector-Valued Singular Integral Operators
The Littlewood-Paley g Function
The Lusin Area Function and the Littlewood-Paley g*[subscript lambda] Function
Hormander's Multiplier Theorem
Notes; Further Results and Problems
The Good [lambda] Principle
Good [lambda] Inequalities
Weighted Norm Inequalities for Maximal CZ Singular Integral Operators
Weighted Weak-Type (1,1) Estimates for CZ Singular Integral Operators
Notes; Further Results and Problems
Hardy Spaces of Several Real Variables
Atomic Decomposition
Maximal Function Characterization of Hardy Spaces
Systems of Conjugate Functions
Multipliers
Interpolation
Notes; Further Results and Problems
Carleson Measures
Carleson Measures
Duals of Hardy Spaces
Tent Spaces
Notes; Further Results and Problems
Cauchy Integrals on Lipschitz Curves
Cauchy Integrals on Lipschitz Curves
Related Operators
The T1 Theorem
Notes; Further Results and Problems
Boundary Value Problems on C[superscript 1]-Domains
The Double and Single Layer Potentials on a C[superscript 1]-Domain
The Dirichlet and Neumann Problems
Notes
Bibliography
Index

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