An FIO-based approach to $L^p$-bounds for the wave equation on $2$-step Carnot groups: the case of Métivier groups

Alessio Martini, Detlef Müller

Let $\mathcal{L}$ be a homogeneous left-invariant sub-Laplacian on a $2$-step Carnot group. We devise a new geometric approach to sharp fixed-time $L^p$-bounds with loss of derivat…