  We establish magnetic improvements upon the classical Hardy inequality for
two specific choices of singular magnetic fields. First, we consider the
Aharonov-Bohm field in all dimensions and establish a sharp Hardy-type
inequality that takes into account both the dimensional as well as the magnetic
flux contributions. Second, in the three-dimensional Euclidean space, we derive
a non-trivial magnetic Hardy inequality for a magnetic field that vanishes at
infinity and diverges along a plane.
