Consider the wave equation associated with the sub-Laplacian on groups of Heisenberg type. We construct parametrices using oscillatory integral representations and use them to prove sharp and Hardy space regularity results.
"Sharp $L^p$ bounds for the wave equation on groups of Heisenberg type." Anal. PDE 8 (5) 1051 - 1100, 2015. https://doi.org/10.2140/apde.2015.8.1051