Some functional inequalities on polynomial volume growth Lie groups
Diego Chamorro

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.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Geometry and complex manifolds · Analytic and geometric function theory
