Restriction type estimates and spectral multipliers on Métivier groups

Lars Niedorf

Published 2023-04-25Version 1

We prove a restriction type estimate for sub-Laplacians on arbitrary two-step stratified Lie groups. Despite being slightly weaker than previously known estimates for the subclass of Heisenberg type groups, these estimates surprisingly turn out to be sufficient to prove an $L^p$-spectral multiplier theorem with sharp regularity condition $s>d\left(1/p-1/2\right)$ for sub-Laplacians on M\'etivier groups, up to some exceptional class in dimension $d=15$.