[Inégalités de Caffarelli–Kohn–Nirenberg étendues et super-poids des inégalités de Hardy Lp-pondérées]
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 , , avec des super-poids.
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 , , with superweights.
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@article{CRMATH_2017__355_6_694_0,
author = {Ruzhansky, Michael and Suragan, Durvudkhan and Yessirkegenov, Nurgissa},
title = {Extended {Caffarelli{\textendash}Kohn{\textendash}Nirenberg} inequalities and superweights for {\protect\emph{L}\protect\textsuperscript{\protect\emph{p}}-weighted} {Hardy} inequalities},
journal = {Comptes Rendus. Math\'ematique},
pages = {694--698},
publisher = {Elsevier},
volume = {355},
number = {6},
year = {2017},
doi = {10.1016/j.crma.2017.04.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2017.04.011/}
}
TY - JOUR AU - Ruzhansky, Michael AU - Suragan, Durvudkhan AU - Yessirkegenov, Nurgissa TI - Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities JO - Comptes Rendus. Mathématique PY - 2017 SP - 694 EP - 698 VL - 355 IS - 6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2017.04.011/ DO - 10.1016/j.crma.2017.04.011 LA - en ID - CRMATH_2017__355_6_694_0 ER -
%0 Journal Article %A Ruzhansky, Michael %A Suragan, Durvudkhan %A Yessirkegenov, Nurgissa %T Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities %J Comptes Rendus. Mathématique %D 2017 %P 694-698 %V 355 %N 6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2017.04.011/ %R 10.1016/j.crma.2017.04.011 %G en %F CRMATH_2017__355_6_694_0
Ruzhansky, Michael; Suragan, Durvudkhan; Yessirkegenov, Nurgissa. Extended Caffarelli–Kohn–Nirenberg inequalities and superweights for Lp-weighted Hardy inequalities. Comptes Rendus. Mathématique, Tome 355 (2017) no. 6, pp. 694-698. doi : 10.1016/j.crma.2017.04.011. http://www.numdam.org/articles/10.1016/j.crma.2017.04.011/
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