Inégalités de Hardy précisées

The aim of this Note is to present 'precised' Hardy-type inequalities. Those inequalities are generalisations of the usual Hardy inequalities, their feature being that they are invariant under oscillations: when applied to highly oscillatory functions, both sides of the precised inequality are of the same order of magnitude. The proof relies on paradifferential calculus and Besov spaces. To cite this article: H. Bahouri et al., C. R. Acad. Sci. Paris, Ser. I 341 (2005).