2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/162050We derive sharp Sobolev inequalities for Sobolev spaces on metric spaces. In particular, we obtain new sharp Sobolev embeddings and Faber-Krahn estimates for Hörmander vector fields.Functional AnalysisAnalysis of PDEsSymmetrization and sharp Sobolev inequalities in metric spacestext