Abstract Hardy-Sobolev spaces and interpolation

Nadine Badr (1) , Frederic Bernicot (2, 3)

1 ICJ - Institut Camille Jordan
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 LPP - Laboratoire Paul Painlevé - UMR 8524

The purpose of this work is to describe an abstract theory of Hardy-Sobolev spaces on doubling Riemannian manifolds via an atomic decomposition. We study the real interpolation of these spaces with Sobolev spaces and finally give applications to Riesz inequalities.

Domaines: Analyse fonctionnelle [math.FA]

Nadine Badr, Frederic Bernicot. Abstract Hardy-Sobolev spaces and interpolation. Journal of Functional Analysis, 2010, pp.1169-1208. ⟨hal-00863715⟩