Functional analysis
Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities
Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 694-698.

In this paper, we give an extension of the classical Caffarelli–Kohn–Nirenberg inequalities with respect to the range of parameters. We also establish best constants for large families of parameters. Moreover, we also obtain anisotropic versions of these inequalities which can be conveniently formulated in the language of Folland and Stein's homogeneous groups. We also establish sharp Hardy type inequalities in $Lp$, $1, with superweights.

Dans cet article, nous donnons une extension des inégalités classiques de Caffarelli–Kohn–Nirenberg relativement à l'étendue du domaine des paramètres. Nous établissons également les meilleures constantes pour les grandes familles de paramètres. De plus, nous obtenons des versions anisotropes de ces inégalités qui peuvent etre commodément formulées dans le langage des groupes homogènes de Folland et Stein. Nous établissons aussi des inégalités de type Hardy dans $Lp$, $1, avec des super-poids.

Accepted:
Published online:
DOI: 10.1016/j.crma.2017.04.011

Michael Ruzhansky 1; Durvudkhan Suragan 2; Nurgissa Yessirkegenov 1

1 Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, United Kingdom
2 Institute of Mathematics and Mathematical Modelling, 125 Pushkin str., Almaty 050010, Kazakhstan
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Michael Ruzhansky; Durvudkhan Suragan; Nurgissa Yessirkegenov. Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities. Comptes Rendus. Mathématique, Volume 355 (2017) no. 6, pp. 694-698. doi : 10.1016/j.crma.2017.04.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.04.011/

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[7] M. Ruzhansky; D. Suragan Layer potentials, Kac's problem, and refined Hardy inequality on homogeneous Carnot groups, Adv. Math., Volume 308 (2017), pp. 483-528

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