Sparse bounds for oscillating multipliers on stratified groups

TL;DR

This paper establishes sparse bounds for spectral multipliers, including oscillating multipliers, on stratified Lie groups, enabling improved weighted bounds for Riesz means and dispersive equations.

Contribution

It introduces novel sparse bounds for oscillating spectral multipliers on stratified groups, extending the scope of harmonic analysis techniques.

Findings

Sparse bounds are proven for a class of spectral multipliers.

Results apply to weighted bounds for Riesz means.

Implications for solutions of dispersive equations.

Abstract

In this article, we address sparse bounds for a class of spectral multipliers that include oscillating multipliers on stratified Lie groups. Our results can be applied to obtain weighted bounds for general Riesz means and for solutions of dispersive equations.