Classical Fourier Analysis (Graduate Texts in Mathematics)
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. Morever, unlike many authors, Grafakos has clearly spent a great deal of time preparing the exercises.” - Ken Ross, MAA OnlineFrom 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. … Classical Fourier Analysis also comes equipped with a wealth of exercise … and each chapter is capped off by a wonderful ‘Historical Notes’ … . I think it’s nigh-on indispensable for the aspiring Fourier analyst." (Michael Berg, MAA Online, January, 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 c)“This book is intended to present the selected topics in depth and to stimulate further study in Fourier analysis. … proofs are provided in great detail and a large amount of exercises of varying difficulty were carefully prepared by the author … . This book is very interesting and useful. It is not only a good textbook, but also an indispensable and valuable reference for researchers … . The readers will certainly benefit a lot from the detailed proofs and the numerous exercises.” (Yang Dachun, Zentralblatt MATH, Vol. 1220, 2011)