2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57517We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.LaTex, 22 pagesMathematical Physics35Q40, 35Q75, 46N50, 81Q10text