Restriction type estimates on general two-step stratified Lie groups

TL;DR

This paper establishes restriction estimates for sub-Laplacians on two-step stratified Lie groups using spectral cluster techniques to analyze eigenvalue distributions of anisotropic twisted Laplacians.

Contribution

It introduces a novel approach employing spectral cluster estimates to derive restriction estimates on general two-step stratified Lie groups.

Findings

Restriction estimates are proved for sub-Laplacians on these groups.

Spectral cluster estimates effectively control eigenvalue distributions.

The approach advances understanding of harmonic analysis on stratified Lie groups.

Abstract

We prove restriction type estimates for sub-Laplacians on general two-step stratified Lie groups. The core of our approach is to use spectral cluster estimates to effectively control the eigenvalue distribution of a family of anisotropic twisted Laplacians.