Weighted restriction type estimates for grushin operators and application to spectral multipliers and bochner-riesz summability

TL;DR

This paper establishes weighted restriction estimates for Grushin operators and applies these results to derive sharp spectral multiplier theorems and Bochner-Riesz summability results, advancing understanding of these operators.

Contribution

It introduces weighted restriction estimates for Grushin operators and uses them to prove sharp spectral multiplier and Bochner-Riesz summability theorems.

Findings

Weighted restriction estimates for Grushin operators.

Sharp spectral multiplier theorems derived.

Optimal Bochner-Riesz summability results obtained.

Abstract

We prove weighted restriction type estimates for Grushin operators. These estimates are then used to prove sharp spectral multiplier theorems as well as Bochner-Riesz summability results with sharp exponent.