Abstract Hardy-Sobolev spaces and interpolation

TL;DR

This paper develops an abstract framework for Hardy-Sobolev spaces on doubling Riemannian manifolds using atomic decompositions, explores their interpolation with Sobolev spaces, and applies findings to Riesz inequalities.

Contribution

It introduces an atomic decomposition approach for Hardy-Sobolev spaces on manifolds and analyzes their interpolation with Sobolev spaces, providing new tools for geometric analysis.

Findings

Atomic decomposition of Hardy-Sobolev spaces established.

Interpolation results between Hardy-Sobolev and Sobolev spaces derived.

Applications to Riesz inequalities demonstrated.

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.