Maximal characterization of Hardy-Sobolev spaces on manifolds

Nadine Badr (1) , Galia Dafni (2)

1 ICJ - Institut Camille Jordan
2 Department of Mathematics and Statistics,Concordia University

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]

Nadine Badr, Galia Dafni. Maximal characterization of Hardy-Sobolev spaces on manifolds. International workshop on concentration, functional inequalities and isoperimetry, Oct 2009, United States. pp.10. ⟨hal-00863455⟩