Some functional inequalities on polynomial volume growth Lie groups

TL;DR

This paper extends Sobolev-type inequalities to polynomial volume growth Lie groups, demonstrating that improved inequalities can be established without Littlewood-Paley decomposition, broadening their applicability in geometric analysis.

Contribution

It introduces a method to prove improved Sobolev inequalities on polynomial volume growth Lie groups without relying on Littlewood-Paley theory.

Findings

Extended Sobolev inequalities to polynomial volume growth Lie groups

Demonstrated inequalities without Littlewood-Paley decomposition

Broadened the scope of functional inequalities in geometric analysis

Abstract

We study in this article some Sobolev-type inequalities on polynomial volume growth Lie groups. We show in particular that improved Sobolev inequalities can be extended without the use of the Littlewood-Paley decomposition to this general framework.