On Spectral multiplier theorem for sub-Laplacians with drift on M\'etivier groups

TL;DR

This paper establishes a spectral multiplier theorem for sub-Laplacians with drift on Métivier groups, improving previous smoothness conditions by reducing the required regularity from homogeneous to topological dimension.

Contribution

It advances the spectral multiplier theory for sub-Laplacians on Métivier groups by weakening the smoothness assumptions needed for the multiplier functions.

Findings

Reduced the smoothness condition from homogeneous to topological dimension.

Extended the spectral multiplier theorem to sub-Laplacians with drift on Métivier groups.

Improved upon previous results by Martini, Ottazzi, and Vallarino.

Abstract

In this paper, we prove a spectral multiplier theorem for sub-Laplacians with drift on M\'etivier groups. We improve the result of [Martini, Ottazzi and Vallarino, Rev. Mat. Iberoam, 2019] in case of M\'etivier groups, by reducing the required smoothness condition on the multiplier function from homogeneous dimension to the topological dimension of the underlying group.