A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields

François Vigneron (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Mots clés: Hardy inequality; Carnot group; Stratified algebra; Commutators; Hypoellliptic vector fields; Hörmander bracket condition

Domaines: Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]; Géométrie différentielle [math.DG]

François Vigneron. A simple proof of the Hardy inequality on Carnot groups and for some hypoelliptic families of vector fields. 2019. ⟨hal-02266609⟩