Abstract Hardy-Sobolev spaces and interpolation

Abstract

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.

34 pages

References in corpus (1)

• Weighted norm inequalities, off-diagonal estimates and elliptic operators. Part I: General operator theory and weights