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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 forthe 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
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 forthe 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
Dieser Download kann aus rechtlichen Gründen nur mit Rechnungsadresse in A, B, BG, CY, CZ, D, DK, EW, E, FIN, F, GR, HR, H, IRL, I, LT, L, LR, M, NL, PL, P, R, S, SLO, SK ausgeliefert werden.
"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)
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 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. ... 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)
"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 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. ... 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)