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Published in:
2011 | OriginalPaper | Chapter
Littlewood–Paley Theory
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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In Chapter 2 we give a detailed presentation on Littlewood-Paley decomposition and define homogeneous and nonhomogeneous Besov spaces. We should emphasize that we have replaced the usual definition of homogeneous spaces (which are quotient distribution spaces modulo polynomials) by something better adapted to the study of partial differential equations (indeed, dealing with distributions modulo polynomials is not appropriate in this context). We also establish technical results (commutator estimates and functional inequalities, in particular) which will be used in the following chapters.