Littlewood-Paley decompositions on manifolds with ends

TL;DR

This paper develops Littlewood-Paley estimates on weighted Lp spaces for non-compact Riemannian manifolds with ends, extending harmonic analysis tools to these geometric settings.

Contribution

It introduces Littlewood-Paley decompositions on manifolds with ends, providing new analytical tools for non-compact geometric analysis.

Findings

Established Littlewood-Paley estimates on weighted Lp spaces

Extended harmonic analysis techniques to manifolds with ends

Provided a framework for analyzing functions on non-compact manifolds

Abstract

For certain non compact Riemannian manifolds with ends, we obtain Littlewood-Paley type estimates on (weighted) Lp spaces, using the usual square function defined by a dyadic partition.