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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.

MSC:

35S50 Paradifferential operators as generalizations of partial differential operators in context of PDEs
26D15 Inequalities for sums, series and integrals
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[1] H. Bahouri, J.-Y. Chemin, I. Gallagher, Precised Hardy inequalities, en préparation · Zbl 1081.35169
[2] Bony, J.-M., Calcul symbolique et propagation des singularités pour LES équations aux dérivées partielles non linéaires, Ann. école normale supérieure de Paris, 14, 209-246, (1981) · Zbl 0495.35024
[3] P. Gérard, Y. Meyer, F. Oru, Inégalités de Sobolev précisées, Séminaire EDP, École Polytechnique, Décembre 1996
[4] Hardy, G.H., Note on a theorem of Hilbert, Math. Z., 6, 314-317, (1920) · JFM 47.0207.01
[5] Hardy, G.H., An inequality between integrals, Messenger math., 54, 150-156, (1925)
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