2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/165994We prove some sharp Hardy inequalities for domains with a spherical symmetry. In particular, we prove an inequality for domains of the unit $n$-dimensional sphere with a point singularity, and an inequality for functions defined on the half-space $\R_+^{n+1}$} vanishing on the hyperplane $\{x_{n+1}=0\}$, with singularity along the $x_{n+1}$-axis. The proofs rely on a one-dimensional Hardy inequality involving a weight function related to the volume element on the sphere, as well as on symmetrization arguments. The one-dimensional inequality is derived in a general form.15 pagesAnalysis of PDEsFunctional Analysis46E35 (Primary) 26D10, 35J25 (Secondary)text