An $L^p$-spectral multiplier theorem with sharp $p$-specific regularity bound on Métivier groups

Lars Niedorf

Published 2022-03-02Version 1

We prove an $L^p$-spectral multiplier theorem for sub-Laplacians on a certain class of two-step stratified Lie groups under the sharp regularity condition $s>d\left(1/p-1/2\right)$, with $d$ being the topological dimension of the underlying group. Our approach relies on restriction type estimates where the multiplier is additionally truncated along the spectrum of the Laplacian on the center of the group.