Real-Variable Methods in Harmonic Analysis

Real-Variable Methods in Harmonic Analysis

by Alberto Torchinsky

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Overview

Real-Variable Methods in Harmonic Analysis by Alberto Torchinsky

"A very good choice." — MathSciNet, American Mathematical Society
An exploration of the unity of several areas in harmonic analysis, this self-contained text emphasizes real-variable methods. Appropriate for advanced undergraduate and graduate students, it starts with classical Fourier series and discusses summability, norm convergence, and conjugate function. An examination of the Hardy-Littlewood maximal function and the Calderón-Zygmund decomposition is followed by explorations of the Hilbert transform and properties of harmonic functions. Additional topics include the Littlewood-Paley theory, good lambda inequalities, atomic decomposition of Hardy spaces, Carleson measures, Cauchy integrals on Lipschitz curves, and boundary value problems. 1986 edition.

Product Details

ISBN-13: 9780486435084
Publisher: Dover Publications
Publication date: 04/09/2004
Series: Dover Books on Mathematics
Pages: 480
Product dimensions: 5.38(w) x 8.50(h) x (d)

Table of Contents

1. Fourier Series
2. Cesaro Summability
3. Norm Convergence of Fourier Series
4. The Basic Principles
5. The Hilbert Transform and Multipliers
6. Paley's Theorem and Fractional Integration
7. Harmonic and Subharmonic Functions
8. Oscillation of Functions
9. Ap Weights
10. More About Rn
11. Calderon-Zygmund Singular Integral Operators
12. The Littlewood-Paley Theory
13. The Good Lambda Principle
14. Hardy Spaces of Several Real Variables
15. Carleson Measures
16. Cauchy Integrals on Lipschitz Curves
17. Boundary Value Problems on C1-Domains
Bibliography
Index

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