Classical Fourier Analysis
Author:   Loukas Grafakos
Publisher:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 3rd ed. 2014
Volume:   249
ISBN:  

9781493939169


Pages:   638
Publication Date:   23 August 2016
Format:   Paperback
Availability:   Manufactured on demand   Availability explained
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Classical Fourier Analysis


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Overview

The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.

Full Product Details

Author:   Loukas Grafakos
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 3rd ed. 2014
Volume:   249
Dimensions:   Width: 15.50cm , Height: 3.40cm , Length: 23.50cm
Weight:   9.767kg
ISBN:  

9781493939169


ISBN 10:   1493939165
Pages:   638
Publication Date:   23 August 2016
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand   Availability explained
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Preface.- 1. Lp Spaces and Interpolation.- 2. Maximal Functions, Fourier Transform, and Distributions.- 3. Fourier Series.- 4. Topics on Fourier Series.- 5. Singular Integrals of Convolution Type.- 6. Littlewood–Paley Theory and Multipliers.- 7. Weighted Inequalities.- A. Gamma and Beta Functions.- B. Bessel Functions.- C. Rademacher Functions.- D. Spherical Coordinates.- E. Some Trigonometric Identities and Inequalities.- F. Summation by Parts.- G. Basic Functional Analysis.- H. The Minimax Lemma.- I. Taylor's and Mean Value Theorem in Several Variables.- J. The Whitney Decomposition of Open Sets in Rn.- Glossary.- References.- Index.

Reviews

“The most up-to-date account of the most important developments in the area. … It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well” (Atanas G. Stefanov, Mathematical Reviews, August, 2015)


The most up-to-date account of the most important developments in the area. ... It has to be pointed out that the hard ones usually come with a good hint, which makes the book suitable for self-study, especially for more motivated students. That being said, the book provides a good reference point for seasoned researchers as well (Atanas G. Stefanov, Mathematical Reviews, August, 2015)


Author Information

Loukas Grafakos is a Professor of Mathematics at the University of Missouri at Columbia.

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