Graduate Texts in Mathematics

Modern Fourier Analysis

Authors: Grafakos, Loukas

  • 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
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Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4939-1230-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-1-4939-1229-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • ISBN 978-1-4939-5078-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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.

About the authors

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

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)


Table of contents (7 chapters)

  • Smoothness and Function Spaces

    Grafakos, Loukas

    Pages 1-53

  • Hardy Spaces, Besov Spaces, and Triebel–Lizorkin Spaces

    Grafakos, Loukas

    Pages 55-152

  • BMO and Carleson Measures

    Grafakos, Loukas

    Pages 153-207

  • Singular Integrals of Nonconvolution Type

    Grafakos, Loukas

    Pages 209-325

  • Boundedness and Convergence of Fourier Integrals

    Grafakos, Loukas

    Pages 327-413

Buy this book

eBook $69.99
price for USA (gross)
  • ISBN 978-1-4939-1230-8
  • Digitally watermarked, DRM-free
  • Included format: PDF, EPUB
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for USA
  • ISBN 978-1-4939-1229-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for USA
  • ISBN 978-1-4939-5078-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Modern Fourier Analysis
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
250
Copyright
2014
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
Distribution Rights
Distribution rights for India: Researchco Book Centre, New Delhi, India
eBook ISBN
978-1-4939-1230-8
DOI
10.1007/978-1-4939-1230-8
Hardcover ISBN
978-1-4939-1229-2
Softcover ISBN
978-1-4939-5078-2
Series ISSN
0072-5285
Edition Number
3
Number of Pages
XVI, 624
Number of Illustrations and Tables
19 b/w illustrations, 1 illustrations in colour
Topics