Yet another criterion for global existence in the 3D relativistic Vlasov-Maxwell system

We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be extended, as long as the quantity $\sigma_{-1}(t, x) = \max_{|\omega|=1} ,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}, \frac{1}{(1+v\cdot\omega)}, f(t, x, p)$isboundedin$L^2_x$.