  In this paper we continue the analysis of the dispersive properties of the 2D
and 3D massless Dirac-Coulomb equations that has been started in
arXiv:1503.00945 and arXiv:2101.07185. We prove a priori estimates of the
solution of the mentioned systems, in particular Strichartz estimates with an
additional angular regularity, exploiting the tools developed in the previous
works. As an application, we show local well-posedness results for a
Dirac-Coulomb equation perturbed with Hartree-type nonlinearities.
