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A simple proof of the
Hardy inequality on Carnot groups and for some hypoelliptic
families of vector fields
François Vigneron |
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Vol. 2 (2020), No. 4, 851–880
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Abstract |
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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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Keywords
Hardy inequality, Carnot group, stratified algebra,
commutators, hypoelliptic vector fields, Hörmander bracket
condition
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Mathematical Subject Classification 2010
Primary: 43A80
Secondary: 35R03, 42B37
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Milestones
Received: 14 August 2019
Accepted: 20 October 2019
Published: 10 December 2019
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Authors |
| François Vigneron | |
| Université Paris-Est LAMA (UMR 8050), UPEC, UPEM, CNRS 61, avenue du Général de Gaulle F94010 Créteil France |
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