Some super-Poincaré inequalities for gaussian-like measures on stratified Lie groups

We continue the $U$-bound program initiated in [J. Funct. Anal. 258, 814-851 (2010)] and prove super-Poincaré inequalities for a class of subelliptic probability measures defined on Métivier groups, the main ingredient in the proof being a Hardy-type inequality. In doing so, we recover and extend some previous results from the probabilistic viewpoint.