Classical Fourier Analysis Van Loukas Grafakos is an English-language textbook that focuses on the theoretical foundations of Fourier analysis in Euclidean spaces. The book is intended for mathematics students who want to explore this field in depth.
It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The presentation is complete and does not leave any theoretical gaps, thereby encouraging deep understanding.
This third edition includes new sections 3.5, 4.4, and 4.5, as well as a chapter on "Weighted Inequalities," taken from GTM 250, 2nd Edition. In addition, Appendices I and B.9 have been added, and numerous corrections and improvements have been made.
The book connects to topics such as functional analysis, complex analysis, and mathematical analysis and is part of the Graduate Texts in Mathematics series.