Riesz means and bilinear Riesz means on Métivier groups

In this paper, we investigate the $L^p$-boundedness of the Riesz means and the $L^{p_1}\times L^{p_2}\to L^p$ boundedness of the bilinear Riesz means on Métivier groups. Métivier groups are generalization of Heisenberg groups and general H-type groups. Because general Métivier groups only satisfy the non-degeneracy condition and have high-dimensional centre, we have to use different methods and techniques from those on Heisenberg groups and H-type groups.