New Calder\'on-Zygmund decompositions

TL;DR

This paper introduces a novel Calderón-Zygmund decomposition for Sobolev spaces on doubling Riemannian manifolds, relaxing previous assumptions by weakening the required hypotheses.

Contribution

It presents a new decomposition method that requires less restrictive conditions than classical approaches based on Poincaré inequalities.

Findings

Decomposition applicable under weaker hypotheses

Extends Calderón-Zygmund theory to broader geometric settings

Provides a foundation for further analysis on Riemannian manifolds

Abstract

We state a new Calderon-Zygmund decomposition for Sobolev spaces on a doubling Riemannian manifold. Our hypotheses are weaker than those of the already known decomposition which used classical Poincare inequalities.