Restriction estimates for the free two step nilpotent group on three generators

TL;DR

This paper analyzes the spectral properties of a sub-Laplacian on a free two-step nilpotent Lie group with three generators, establishing a Tomas-Stein type estimate for associated operators.

Contribution

It computes the spectral resolution of the sub-Laplacian on this specific nilpotent group and proves a new Tomas-Stein type estimate for the resulting operators.

Findings

Spectral resolution of the sub-Laplacian is explicitly computed.

Operators satisfy a Tomas-Stein type estimate.

Advances understanding of harmonic analysis on nilpotent Lie groups.

Abstract

Let $G$ be the free two step nilpotent Lie group on three generators and let $L$ be a sub-Laplacian on it. We compute the spectral resolution of $L$ and prove that the operators arising from this decomposition enjoy a Tomas-Stein type estimate.