A counterexample for Improved Sobolev Inequalities over the 2-adic group

Diego Chamorro (1)

1 LAP - Laboratoire Analyse et Probabilités

On the framework of the 2-adic group Z_2, we study a Sobolev-like inequality where we estimate the L^2 norm by a geometric mean of the BV norm and the Besov space B(-1,\infty,\infty) norm. We first show, using the special topological properties of the p-adic groups, that the set of functions of bounded variations BV can be identified to the Besov space B(1,\infty,1). This identification lead us to the construction of a counterexample to the improved Sobolev inequality.

Mots clés: Sobolev inequalities; p-adic groups

Domaines: Equations aux dérivées partielles [math.AP]; Analyse fonctionnelle [math.FA]

Diego Chamorro. A counterexample for Improved Sobolev Inequalities over the 2-adic group. 2010. ⟨hal-00531555⟩