Restriction type estimates on general two-step 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.

This revised submission represents Part 1 of the paper previously submitted as arXiv:2304.12960. The original submission has been split into two separate papers to provide a clearer presentation of the results. Part 2 has been submitted separately. Added a funding acknowledgment in the latest version