Littlewood–Paley Theory

  • Hajer BahouriEmail author
  • Jean-Yves Chemin
  • Raphaël Danchin
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 343)


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.


Positive Real Number Besov Space Lebesgue Space Theory Proof Fourier Multiplier 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Hajer Bahouri
    • 1
    Email author
  • Jean-Yves Chemin
    • 2
  • Raphaël Danchin
    • 3
  1. 1.Départment de Mathématiques, Faculté des Sciences de Tunis, Campus UniversitaireUniversité de Tunis El ManarTunisTunisia
  2. 2.Laboratoire Jacques-Louis LionsUniversité Pierre et Marie CurieParis Cedex 05France
  3. 3.Centre de Mathématiques, Faculté de Sciences et TechnologieUniversité Paris XII-Val de MarneCréteil CedexFrance

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