2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/119450In this paper we prove sharp weighted Hardy-type inequalities on Carnot groups with the homogeneous norm $N=u^{1/(2-Q)}$ associated to Folland's fundamental solution $u$ for the sub-Laplacian $Δ_{\mathbb{G}}$. We also prove uncertainty principle, Caffarelli-Kohn-Nirenberg and Rellich inequalities on Carnot groups.Functional AnalysisClassical Analysis and ODEs22E30, 43A80, 26D10text