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Macmillan Higher Education Palgrave Higher Education

Modern Fourier Analysis

Edition 3rd Edition
ISBN 9781493912292
Publication Date November 2014
Formats Hardcover Paperback Ebook 
Publisher Springer

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.

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

Smoothness and Function Spaces
BMO and Carleson Measures
Singular Integrals of Nonconvolution Type
Weighted Inequalities
Boundedness and Convergence of Fourier Integrals
Time-Frequency Analysis and the Carleson-Hunt Theorem
Multilinear Harmonic Analysis


“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)
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