卡诺群上Hardy不等式的一个简单证明和一些次椭圆向量场族的证明

IF 0.8 Q2 MATHEMATICS Tunisian Journal of Mathematics Pub Date : 2019-08-19 DOI:10.2140/tunis.2020.2.851
Franccois Vigneron
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引用次数: 1

摘要

我们给出了任何卡诺群上的经典Hardy不等式的一个初等证明,只使用部分积分和对换向器结构的精细分析,这直到现在才被认为是可能的。我们还讨论了这种技术可以推广到处理向量场的次椭圆族的条件,在这种情况下,这导致了关于规范范数的符号性质的一个开放问题。
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A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields
We give an elementary proof of the classical Hardy inequality on any Carnot group, using only integration by parts and a fine analysis of the commutator structure, which was not deemed possible until now. We also discuss the conditions under which this technique can be generalized to deal with hypoelliptic families of vector fields, which, in this case, leads to an open problem regarding the symbol properties of the gauge norm.
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来源期刊
Tunisian Journal of Mathematics
Tunisian Journal of Mathematics Mathematics-Mathematics (all)
CiteScore
1.70
自引率
0.00%
发文量
12
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