On critical cases of Sobolev's inequalities for Carnot groups
首发时间:2011-05-20
Abstract: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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Carnot群上临界情形的Sobolev不等式
摘要:本文主要考虑在一般的Carnot幂零李群上临界情形的Sobolev嵌入问题。我们证明了在整个Carnot群上存在一类 Trudinger型不等式,这一点推广了由T. Ozawa所证明的欧式空间和本文作者所证明的Heisenberg群情形。该证明过程依赖于一类Gagliardo-Nirenberg不等式的估计。在本文还得到了一个新的嵌入不等式,利用该不等式,文献[1]中定理1.4的条件 m>max{Q/q,1} 可以改进为 m>Q/q. 进一步利用上述不等式,我们还得到了Carnot群上的Brezis-Gallouet-Wainger不等式。
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No.4426810509842130****
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