  This paper is concerned with the asymptotic properties of the small data
solutions to the massless Vlasov-Maxwell system in $3d$. We use vector field
methods to derive almost optimal decay estimates in null directions for the
electromagnetic field, the particle density and their derivatives. No compact
support assumption in $x$ or $v$ is required on the initial data and the decay
in $v$ is in particular initially optimal. Consistently with Proposition $8.1$
of \cite{dim4}, the Vlasov field is supposed to vanish initially for small
velocties. In order to deal with the slow decay rate of the solutions near the
light cone and to prove that the velocity support of the particle density
remains bounded away from $0$, we make crucial use of the null properties of
the system.

Analysis of PDEs