Synopses & Reviews
"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.
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.
This text starts with Fourier series, summability, norm convergence, and conjugate function. Additional topics include Hilbert transform, Paley theory, Cauchy integrals on Lipschitz curves, and boundary value problems. 1986 edition.
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