© 2014

Classical Fourier Analysis


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

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Loukas Grafakos
    Pages 1-83
  3. Loukas Grafakos
    Pages 173-240
  4. Loukas Grafakos
    Pages 241-311
  5. Loukas Grafakos
    Pages 313-417
  6. Loukas Grafakos
    Pages 419-498
  7. Loukas Grafakos
    Pages 499-561
  8. Back Matter
    Pages 563-638

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.

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


Bessel Functions Gibbs phenomenon Littlewood-Paley Theory Spherical Fourier inversion Tauberian theorems classical fourier analysis functional analysis

Authors and affiliations

  1. 1.Department of MathematicsUniversity of MissouriColumbiaUSA

About the authors

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

Bibliographic information


“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)