Sub-elliptic global high order Poincaré inequalities in stratified Lie groups and applications (Q996252)

The authors prove higher order Poincaré inequalities on a stratified Lie group \(\mathbb{G}\), with explicit proof for the particular case of first order Poincaré inequalities. Also, the authors derive a weighted version of higher order Poincaré inequalities on a Lie group \(\mathbb{G}\) under a balance condition of weights. The last part of the paper deals with high order Poincaré inequalities on unbounded extension domains.