Precised Hardy inequalities. (Inégalités de Hardy précisées.) (French) Zbl 1081.35169

Summary: We present ‘precised’ Hardy-type inequalities. These inequalities are generalizations 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.


35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
26D15 Inequalities for sums, series and integrals
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