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

TL;DR

This paper establishes sharp weighted $L^p$ bounds for Grushin pseudo-multipliers satisfying Hörmander's condition, using sparse domination techniques to improve understanding of their boundedness properties.

Contribution

It introduces a novel approach to bounding Grushin pseudo-multipliers via sparse operators, providing sharp quantitative weighted estimates.

Findings

Sharp weighted $L^p$ bounds for Grushin pseudo-multipliers

Pointwise domination of pseudo-multipliers by sparse operators

Enhanced understanding of pseudo-multiplier boundedness

Abstract

In this article, we prove sharp quantitative weighted $L^p$-estimates for Grushin pseudo-multipliers satisfying H\"ormander's condition as an application of pointwise domination of Grushin pseudo-multipliers by appropriate sparse operators.