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Modern 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, "Multilinear Harmonic Analysis", including sections on multilinear operators, multilinear interpolation, multilinear multiplier operators, Calderón-Zygmund operators of several functions and multiple weights and weighted norm inequalities
  • 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:
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Part of the book series: Graduate Texts in Mathematics (GTM, volume 250)

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About this book

This text is aimed at graduate students in mathematics and to interested researchers who wish to acquire an in depth understanding of Euclidean Harmonic analysis. The text covers modern topics and techniques in function spaces, atomic decompositions, singular integrals of nonconvolution type and the boundedness and convergence of Fourier series and integrals. The exposition and style are designed to stimulate further study and promote research. Historical information and references are included at the end of each chapter.

This third edition includes a new chapter entitled "Multilinear Harmonic Analysis" which focuses on topics related to multilinear operators and their applications. Sections 1.1 and 1.2 are also new in this edition. Numerous corrections have been made to the text from the previous editions and several improvements have been incorporated, such as the adoption of clear and elegant statements. A few more exercises have been added with relevant hints when necessary.

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Table of contents (7 chapters)


“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

  • Mathematics Department, 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: Modern 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: 978-1-4939-1229-2Published: 14 November 2014

  • Softcover ISBN: 978-1-4939-5078-2Published: 23 August 2016

  • eBook ISBN: 978-1-4939-1230-8Published: 13 November 2014

  • Series ISSN: 0072-5285

  • Series E-ISSN: 2197-5612

  • Edition Number: 3

  • Number of Pages: XVI, 624

  • Number of Illustrations: 19 b/w illustrations, 1 illustrations in colour

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

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