Lie Algebras/Partial Differential Equations
Sharp weighted Hardy type inequalities and Hardy–Sobolev type inequalities on polarizable Carnot groups
Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1231-1234.

In this Note, we establish sharp weighted Hardy type inequalities with a more general index p on polarizable Carnot groups, which include Kombe's recent results; then a weighted Hardy–Sobolev type inequality is obtained by using previous inequalities.

Dans cette Note nous établissons des inégalités optimales de type de Hardy avec poids dans le cas d'indices p plus généraux sur des groupes de Carnot polarisables ; nos résultats contiennent ceux obtenus récemment par Kombe. À partir des résultats précédemment établis nous démontrons une inégalité de type Hardy–Sobolev avec poids.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2008.10.009
Wang, Jialin 1; Niu, Pengcheng 1

1 Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, Shaanxi, PR China
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Wang, Jialin; Niu, Pengcheng. Sharp weighted Hardy type inequalities and Hardy–Sobolev type inequalities on polarizable Carnot groups. Comptes Rendus. Mathématique, Volume 346 (2008) no. 23-24, pp. 1231-1234. doi : 10.1016/j.crma.2008.10.009. http://www.numdam.org/articles/10.1016/j.crma.2008.10.009/

[1] Balogh, Z.-M.; Tyson, J.-T. Polar coordinates in the Carnot groups, Math. Z., Volume 241 (2002), pp. 697-730

[2] Folland, G.-B. Subelliptic estimates and function spaces on nilpotent Lie groups, Arkiv. Math., Volume 13 (1975), pp. 161-207

[3] Han, Y.; Niu, P. Hardy–Sobolev type inequalities on the H-type Group, Manuscripta Math., Volume 211 (2005), pp. 235-252

[4] Kombe, I. The Hardy inequality and nonlinear parabolic equations on Carnot groups (pp. 1–12) | arXiv

[5] Kombe, I. Hardy, Rellich and uncertainty principle inequalities on Carnot groups (pp. 1-19) | arXiv

[6] Tyson, J.-T. Sharp weighted Young's inequalities and Moser–Trudinger inequalities on Heisenberg type groups and Grushin spaces, Potential Anal., Volume 24 (2006), pp. 357-384

Cited by Sources:

This work was supported by the National Natural Science Foundation of China (Grant No. 10871157) and Keji Chuangxin Jijin of Northwestern Polytechnical University, No. 2007KJ01012.