Comptes Rendus
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

Jialin Wang 1; Pengcheng Niu 1

1 Department of Applied Mathematics, Northwestern Polytechnical University, 710072, Xi'an, Shaanxi, PR China
@article{CRMATH_2008__346_23-24_1231_0,
     author = {Jialin Wang and Pengcheng Niu},
     title = {Sharp weighted {Hardy} type inequalities and {Hardy{\textendash}Sobolev} type inequalities on polarizable {Carnot} groups},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1231--1234},
     publisher = {Elsevier},
     volume = {346},
     number = {23-24},
     year = {2008},
     doi = {10.1016/j.crma.2008.10.009},
     language = {en},
}
TY  - JOUR
AU  - Jialin Wang
AU  - Pengcheng Niu
TI  - Sharp weighted Hardy type inequalities and Hardy–Sobolev type inequalities on polarizable Carnot groups
JO  - Comptes Rendus. Mathématique
PY  - 2008
SP  - 1231
EP  - 1234
VL  - 346
IS  - 23-24
PB  - Elsevier
DO  - 10.1016/j.crma.2008.10.009
LA  - en
ID  - CRMATH_2008__346_23-24_1231_0
ER  - 
%0 Journal Article
%A Jialin Wang
%A Pengcheng Niu
%T Sharp weighted Hardy type inequalities and Hardy–Sobolev type inequalities on polarizable Carnot groups
%J Comptes Rendus. Mathématique
%D 2008
%P 1231-1234
%V 346
%N 23-24
%I Elsevier
%R 10.1016/j.crma.2008.10.009
%G en
%F CRMATH_2008__346_23-24_1231_0
Jialin Wang; Pengcheng Niu. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.10.009/

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

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

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

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

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

[6] J.-T. Tyson 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.

Comments - Policy