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

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.

Keywords

maximal inequalities, Sobolev spaces, interpolation

2010 Mathematics Subject Classification

42B25, 46B70, 46E35

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Published 1 January 2009