Sparse bounds for pseudo-multipliers associated to Grushin operators, II

TL;DR

This paper proves pointwise sparse domination for Grushin pseudo-multipliers across various symbol classes, enabling the derivation of quantitative weighted estimates, thus advancing the understanding of these operators in harmonic analysis.

Contribution

It extends previous work by establishing new sparse bounds for Grushin pseudo-multipliers, providing a unified framework for weighted estimates in this context.

Findings

Established pointwise sparse domination results for Grushin pseudo-multipliers.

Derived quantitative weighted estimates from the sparse bounds.

Extended the analysis to various symbol classes.

Abstract

In this article, we establish pointwise sparse domination results for Grushin pseudo-multipliers corresponding to various symbol classes, as a continuation of our investigation initiated in [BBGG21]. As a consequence, we deduce quantitative weighted estimates for these pseudo-multipliers.