  In this paper, we present sharp decay estimates for small data solutions of
the following two systems: the Vlasov-Poisson (V-P) system in dimension 3 or
higher and the Vlasov-Yukawa (V-Y) system in dimension 2 or higher. We rely on
a modification of the vector field method for transport equation as developed
by Smulevici in 2016 for the Vlasov-Poisson system. Using the Green's function
in particular to estimate bilinear terms, we improve Smulevici's result by
requiring only $L^1_{x,v}$ bounds for the initial data and its derivatives. We
also extend the result to the Vlasov-Yukawa system.
