  This article deals with kinetic Fokker-Planck equations with essentially
bounded coefficients. A weak Harnack inequality for non-negative
super-solutions is derived by considering their Log-transform and following S.
N. Kruzhkov (1963). Such a result rests on a new weak Poincar{\'e} inequality
sharing similarities with the one introduced by W. Wang and L. Zhang in a
series of works about ultraparabolic equations (2009, 2011, 2017). This
functional inequality is combined with a classical covering argument recently
adapted by L. Silvestre and the second author (2020) to kinetic equations.
