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On critical cases of Sobolev's inequalities for Heisenberg groups
Yang Qiaohua * #
School of Mathematics and Statistics, Wuhan University
*Correspondence author
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Funding: This work was supported by the Doctoral Fund for New Teachers （No.No.20090141120008）, the Fundamental Research Funds for the Central Universities under Grant（No.No. 1082001）
Opened online:21 September 2010
Accepted by: none
Citation: Yang Qiaohua.On critical cases of Sobolev's inequalities for Heisenberg groups[OL]. [21 September 2010] http://en.paper.edu.cn/en_releasepaper/content/4385626
 
 
This paper deal with the problem of Sobolev imbedding in the critical cases. We prove some Trudinger-type inequalities on the whole Heisenberg group, extending to this context the Euclidean results by T. Ozawa. The procedue depend on optimal growth rate of Gagliardo-Nirenberg inequalities. We obtain the sharp constant for the Trudinger-type inequalities on the whole Heisenberg groups when the function is radial. Using these inequalities, the estimate of heat kernel and the Reisz transform, we obtain some Morrey's inequality and the Brezis-Gallouet-Wainger inequality.
Keywords:Heisenberg group;Sobolev's inequality; Brezis-Gallouet-Wainger inequality
 
 
 

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