2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114251In this paper we prove sharp Hardy inequalities by using Maximal function theory. Our results improve and extend the well-known results of G.Hardy \cite{Ha04}, T.Cazenave \cite {Ca03}, J.-Y.Chemin\cite {Ch06} and T.Tao\cite {TT06}.6 pagesAnalysis of PDEs42B25text