  We 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.
