Hardy and uncertainty inequalities on stratified Lie groups

We prove various Hardy-type and uncertainty inequalities on a stratified Lie group G  . In particular, we show that the operators Tα:f↦|⋅|−αL−α/2fTα:f↦|⋅|−αL−α/2f, where |⋅||⋅| is a homogeneous norm, 0<α