The Calder\'on-Zygmund inequalities on evolving Riemannian manifolds

TL;DR

This paper extends Calderón-Zygmund inequalities to evolving Riemannian manifolds with bounded curvature, providing foundational results and applications in harmonic analysis and PDEs.

Contribution

It introduces Calderón-Zygmund inequalities on evolving manifolds with bounded curvature, a novel extension in geometric analysis.

Findings

Established Calderón-Zygmund inequalities on evolving Riemannian manifolds

Provided applications demonstrating the utility of these inequalities

Extended classical harmonic analysis tools to dynamic geometric settings

Abstract

The Calder\'on-Zygmund inequality is a cornerstone of harmonic analysis and partial differential equations. In this article, we establish various Calder\'on-Zygmund inequalities on evolving Riemannian manifolds with bounded curvature. We also provide concrete applications of such inequalities.