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

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