Maximal characterization of Hardy-Sobolev spaces on manifolds
Résumé
Let $M$ be a complete non-compact Riemannian manifold with a doubling measure and admitting a Poincaré inequality. In the present paper, we identify the Sobolev space $\dot{M}^1_1$, introduced by Haj{\l}asz, with a new Hardy-Sobolev space defined by requiring the integrability of a certain maximal function of the gradient. This completes the circle of ideas begun in \cite{badrdafni}, where $\dot{M}^1_1$ was identified with a Hardy-Sobolev space via atomic decomposition.
Domaines
Analyse fonctionnelle [math.FA]
Origine : Fichiers produits par l'(les) auteur(s)
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