Modern Fourier Analysis

• Smoothness and Function Spaces.- and Carleson Measures.- Singular Integrals of Nonconvolution Type.- Weighted Inequalities.- Boundedness and Convergence of Fourier Integrals.- Time Frequency Analysis and the Carleson#x2013;Hunt Theorem.

From a reviews: "Grafakos's book is very user-friendly with numerous examples illustrating the definitions and ideas. It is more suitable for readers who want to get a feel for current research. The treatment is thoroughly modern with free use of operators and functional analysis. Moreover, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises." - Ken Ross, MAA Online From the reviews of the second edition: "The author ... has produced a very well-written, polished, and exciting graduate textbook which easily doubles as a reference book in a number of areas belonging to or touching on Fourier analysis. ... Modern Fourier Analysis sports a huge number off well-designed problems and exercises, and every chapter ends with an exceedingly informative set of 'Historical Notes'. ... I think it's nigh-on indispensable for the aspiring Fourier analyst." (Michael Berg, MAA Online, January, 2009) "The second part of the two volume treatise in harmonic analysis entitled 'Modern Fourier Analysis' is designed to be a continuation of the first volume ... . The historical notes in each chapter are intended to provide an account of past research as well as to suggest directions for further investigation. The volume is mainly addressed to graduate students who wish to study harmonic analysis." (Leonid Golinskii, Zentralblatt MATH, Vol. 1158, 2009) "Intended for graduate students who wish to study Fourier analysis. ... also suitable for self-study. Proofs are provided in great detail. Each chapter is followed by historical notes with references, often including a discussion of further results. There are numerous exercises of varying difficulty, with hints and references provided for the harder ones. ... 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 Seeger, Mathematical Reviews, Issue 2011 d)