Classical Fourier Analysis: Prelimianry Entry 249 (Graduate by Loukas Grafakos

By Loukas Grafakos

the first target of this article is to offer the theoretical beginning of the sector of Fourier research. This e-book is principally addressed to graduate scholars in arithmetic and is designed to serve for a three-course series at the topic. the single prerequisite for realizing the textual content is passable finishing touch of a direction in degree concept, Lebesgue integration, and intricate variables. This ebook is meant to offer the chosen subject matters in a few intensity and stimulate extra research. even though the emphasis falls on genuine variable tools in Euclidean areas, a bankruptcy is dedicated to the basics of research at the torus. This fabric is incorporated for historic purposes, because the genesis of Fourier research are available in trigonometric expansions of periodic capabilities in different variables.While the first version was once released as a unmarried quantity, the recent variation will include a hundred and twenty pp of latest fabric, with an extra bankruptcy on time-frequency research and different sleek issues. hence, the e-book is now being released in 2 separate volumes, the 1st quantity containing the classical themes (Lp areas, Littlewood-Paley conception, Smoothness, etc...), the second one quantity containing the fashionable issues (weighted inequalities, wavelets, atomic decomposition, etc...).From a overview of the 1st edition:“Grafakos’s publication is particularly effortless with quite a few examples illustrating the definitions and ideas. it really is greater for readers who are looking to get a suppose for present study. The therapy is punctiliously smooth with loose use of operators and sensible research. Morever, in contrast to many authors, Grafakos has basically spent loads of time getting ready the exercises.” - Ken Ross, MAA Online

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