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Classical Fourier Analysis

  • Textbook
  • © 2014
  • Latest edition


  • New edition extensively revised and updated, including 1000 different corrections and improvements in the existing text
  • Includes a new chapter, "Topics on Fourier series", including sections on Gibbs phenomenon, summability methods and Jackson's theorem, Tauberian theorems, spherical Fourier inversion, and Fourier transforms on the line
  • Provides motivation for the reader with more examples and applications, new and more relevant hints for the existing exercises, and about 20-30 new exercises in the existing chapters
  • Includes supplementary material:
  • Request lecturer material:

Part of the book series: Graduate Texts in Mathematics (GTM, volume 249)

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Table of contents (7 chapters)


About this book

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.


“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)

Authors and Affiliations

  • Department of Mathematics, University of Missouri, Columbia, USA

    Loukas Grafakos

About the author

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

Bibliographic Information

  • Book Title: Classical Fourier Analysis

  • Authors: Loukas Grafakos

  • Series Title: Graduate Texts in Mathematics

  • DOI:

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2014

  • Hardcover ISBN: 978-1-4939-1193-6Published: 19 November 2014

  • Softcover ISBN: 978-1-4939-3916-9Published: 23 August 2016

  • eBook ISBN: 978-1-4939-1194-3Published: 17 November 2014

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XVII, 638

  • Number of Illustrations: 12 b/w illustrations, 2 illustrations in colour

  • Topics: Fourier Analysis, Abstract Harmonic Analysis, Functional Analysis

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