Maximal inequalities for dual Sobolev spaces $W^{-1,p}$ and applications to interpolation

Frédéric Bernicot (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We firstly describe a maximal inequality for dual Sobolev spaces W^{-1,p}. This one corresponds to a "Sobolev version" of usual properties of the Hardy-Littlewood maximal operator in Lebesgue spaces. Even in the euclidean space, this one seems to be new and we develop arguments in the general framework of Riemannian manifold. Then we present an application to obtain interpolation results for Sobolev spaces.

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

Frédéric Bernicot. Maximal inequalities for dual Sobolev spaces $W^{-1,p}$ and applications to interpolation. Mathematical Research Letters, 2009, 16 (5), pp.763-778. ⟨hal-00349246⟩