$q$-Poincar\'e inequalities on Carnot Groups with filiform type Lie algebra

TL;DR

This paper establishes global q-Poincaré inequalities for probability measures on nilpotent Lie groups with filiform Lie algebra, extending functional inequalities in geometric analysis.

Contribution

It proves q-Poincaré inequalities for a broad class of measures on nilpotent Lie groups with filiform Lie algebra, generalizing previous results.

Findings

Proved global q-Poincaré inequalities for measures with densities depending on homogeneous norms.

Extended functional inequalities to nilpotent Lie groups with filiform Lie algebra.

Applicable to probability measures with specific density functions.

Abstract

In this paper, we prove (global) $q$-Poincar\'e 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.