$q$-Poincaré inequalities on Carnot Groups with filiform type Lie algebra

Abstract

In this paper, we prove (global) $q$-Poincaré inequalities for probability measures on nilpotent Lie groups with filiform Lie algebra of any length. The probability measures under consideration have a density with respect to the Haar measure given as a function of a suitable homogeneous norm.

arXiv comment29 pages