# A multiplier theorem for sub-Laplacians with drift on Lie groups

## TL;DR

This paper establishes a broad multiplier theorem for sub-Laplacians with drift on non-compact Lie groups, enhancing previous results and applicable to various group structures including polynomial growth and solvable extensions.

## Contribution

It introduces a general multiplier theorem for symmetric left-invariant sub-Laplacians with drift on Lie groups, extending prior work significantly.

## Key findings

- Proves a comprehensive multiplier theorem for sub-Laplacians with drift.
- Extends previous results to groups of polynomial growth and solvable extensions.
- Improves the applicability of multiplier theorems in Lie group analysis.

## Abstract

We prove a general multiplier theorem for symmetric left-invariant sub-Laplacians with drift on non-compact Lie groups. This considerably improves and extends a result by Hebisch, Mauceri, and Meda. Applications include groups of polynomial growth and solvable extensions of stratified groups.