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On critical cases of Sobolev's inequalities for Carnot groups
Yang Qiaohua * #
School of Mathematics and Statistics, Wuhan University
*Correspondence author
#Submitted by
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Funding: Fundamental Research Funds for the Central Universities under Grant （No.No. 1082001）
Opened online:20 May 2011
Accepted by: none
Citation: Yang Qiaohua.On critical cases of Sobolev's inequalities for Carnot groups[OL]. [20 May 2011] http://en.paper.edu.cn/en_releasepaper/content/4426810
 
 
In this paper we deal with the problem of Sobolev imbedding in thecritical cases on Carnot groups. We prove some Trudinger-type inequalities on the whole Carnot group, extending to this context the Euclidean results by T. Ozawa and the Heisenberg groups by the same author. The procedure depend also on optimal growth rate of Gagliardo-Nirenberg inequalities. We note the condition m>max{Q/q,1} in [1], Theorem 1.4, can be replaced by m>Q/q though a new inequality on G. Using these inequalities, we also obtain the Brezis-Gallouet-Wainger inequality on Carnot group.
Keywords:Carnot group; Sobolev's inequality; Brezis-Gallouet-Wainger inequality
 
 
 

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