Sharp spectral multipliers for a new class of Grushin type operators

TL;DR

This paper establishes sharp spectral multiplier results and weighted Plancherel estimates for a novel class of Grushin type operators, advancing the understanding of their harmonic analysis properties.

Contribution

It introduces new spectral multiplier theorems and optimal Bochner-Riesz summability exponents for a previously unexplored class of Grushin operators.

Findings

Established weighted Plancherel estimates

Proved sharp spectral multiplier theorems

Determined optimal Bochner-Riesz exponents

Abstract

We describe weighted Plancherel estimates and sharp Hebisch-M\"uller-Stein type spectral multiplier result for a new class of Grushin type operators. We also discuss the optimal exponent for Bochner-Riesz summability in this setting.