عنوان

Classical Fourier analysis /

(Number (ISBN

1493911937

(Number (ISBN

1493911945

(Number (ISBN

9781493911936

(Number (ISBN

9781493911943

Erroneous ISBN

9781493911936

Number

b623734

Title Proper

Classical Fourier analysis /

General Material Designation

[Book]

First Statement of Responsibility

Loukas Grafakos.

Edition Statement

Third edition.

Specific Material Designation and Extent of Item

1 online resource (xvii, 638 pages) :

Other Physical Details

illustrations

Series Title

Graduate texts in mathematics ;

Volume Designation

249

Text of Note

Includes bibliographical references and index.

Text of Note

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.

0

Text of Note

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. Reviews from the Second Edition: "The books cover a large amount of mathematics. They are certainly a valuable and useful addition to the existing literature and can serve as textbooks or as reference books. Students will especially appreciate the extensive collection of exercises."--Andreas Seager, Mathematical Reviews "This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers who are working on analysis and partial differential equations. The readers will certainly benefit a lot from the detailed proofs and the numerous exercises."--Yang Dachun, zbMATH--

Source for Acquisition/Subscription Address

Springer

International Standard Book Number

9781493911936

Fourier analysis.

Fourier, Analyse de.

Fourier analysis.

Harmonische Analyse

MAT034000

PBKF

PBKF

Number

Edition

Class number

Grafakos, Loukas

Date of Transaction

20200617082839.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y