Some super-Poincar\'e 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-Poincar\'e inequalities for a class of probability measures defined on stratified Lie groups and in terms of their homogeneous norms with explicit estimates, 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.