2011 | OriginalPaper | Chapter
Basic Analysis
Authors : Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin
Published in: Fourier Analysis and Nonlinear Partial Differential Equations
Publisher: Springer Berlin Heidelberg
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Chapter 1 is devoted to a self-contained elementary presentation of classical Fourier analysis results. Even though none of the results are new, some of the proofs that we present are not the standard ones and are likely to be useful in other contexts. We also pay attention to the construction of explicit examples which illustrate the optimality of some refined estimates.