Sobolev spaces on multiple cones

Pascal Auscher (1) , Nadine Badr (2)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay
2 ICJ - Institut Camille Jordan

The purpose of this note is to discuss how various Sobolev spaces defined on multiple cones behave with respect to density of smooth functions, interpolation and extension/restriction to/from $\RR^n$. The analysis interestingly combines use of Poincaré inequalities and of some Hardy type inequalities.

Mots clés: Sobolev spaces; Poincaré inequality; Doubling property; Metric-measure spaces; Calderón-Zygmund decomposition; Calderón-Zygmund decomposition.

Domaines: Analyse classique [math.CA]; Analyse fonctionnelle [math.FA]; Géométrie métrique [math.MG]

Pascal Auscher, Nadine Badr. Sobolev spaces on multiple cones. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2010, 19 (3-4), pp.707-733. ⟨hal-00344706v4⟩