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3 Local Warehouse Mathematics- Harmonic Analysis

Real-Variable Methods in Harmonic Analysis (Dover Books on Mathematics)

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Real-Variable Methods in Harmonic Analysis (Dover Books on Mathematics) Cover

 

Synopses & Reviews

Publisher Comments:

"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.

Book News Annotation:

As an introduction to harmonic analysis for graduate students, Torchinsky (Indiana University) examines the convergence of Fourier series of functions and distributions, then develops the Muckenhoupt theory of Ap weights, the Calderon-Zygmund theory of singular integral operators, the Littlewood-Paley theory, and the Fefferman- Stein theory of Hardy spaces. Originally published by Academic Press in 1986 as part of the Pure and applied mathematics series.
Annotation 2004 Book News, Inc., Portland, OR (booknews.com)

Synopsis:

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.

Synopsis:

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.

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

Product Details

ISBN:
9780486435084
Author:
Torchinsky, Alberto
Publisher:
Dover Publications
Author:
Mathematics
Location:
Mineola, N.Y.
Subject:
General
Subject:
Infinity
Subject:
Harmonic analysis
Subject:
General Mathematics
Subject:
Functional Analysis
Subject:
Mathematics - General
Copyright:
Edition Description:
Trade Paper
Series:
Dover Books on Mathematics
Series Volume:
PRB 02-36F
Publication Date:
20040431
Binding:
TRADE PAPER
Language:
English
Illustrations:
Y
Pages:
480
Dimensions:
8.5 x 5.38 in 1.11 lb

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Product details 480 pages Dover Publications - English 9780486435084 Reviews:
"Synopsis" by ,
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.

"Synopsis" by ,
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.

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