Higher order coercive inequalities on nilpotent Lie groups

TL;DR

This paper investigates advanced inequalities related to regularity of Markov generators on nilpotent Lie groups, contributing to the understanding of functional analysis in probabilistic and geometric contexts.

Contribution

It introduces higher order coercive inequalities specific to nilpotent Lie groups, advancing the theoretical framework for analyzing Markov generators.

Findings

Established new higher order coercive inequalities

Enhanced understanding of regularity properties of Markov generators

Extended analysis techniques to nilpotent Lie group settings

Abstract

In this work, we study regularity problems of certain Markov generators, which naturally appear in the context of analysis in functional spaces associated to probability measures on nilpotent Lie groups.