An atomic decomposition of the Haj{\l}asz Sobolev space $\Mone$ on manifolds

Nadine Badr (1) , Galia Dafni (2)

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

Several possible notions of Hardy-Sobolev spaces on a Riemannian manifold with a doubling measure are considered. Under the assumption of a Poincaré inequality, the space $\Mone$, defined by Haj{\l}asz, is identified with a Hardy-Sobolev space defined in terms of atoms. Decomposition results are proved for both the homogeneous and the nonhomogeneous spaces.

Mots clés: Hardy-Sobolev spaces; atomic decomposition; metric measure spaces; Hajłasz-Sobolev spaces

Domaines: Géométrie différentielle [math.DG]; Analyse fonctionnelle [math.FA]

Nadine Badr, Galia Dafni. An atomic decomposition of the Haj{\l}asz Sobolev space $\Mone$ on manifolds. Journal of Functional Analysis, 2010, 259 (6), pp.1380-1420. ⟨hal-00424406v2⟩