  We prove Landau damping for the collisionless Vlasov equation with a class of
$L^1$ interaction potentials (including the physical case of screened Coulomb
interactions) on $\mathbb R^3_x \times \mathbb R^3_v$ for localized
disturbances of an infinite, homogeneous background. Unlike the confined case
$\mathbb T^3_x \times \mathbb R_v^3$, results are obtained for initial data in
Sobolev spaces (as well as Gevrey and analytic classes). For spatial
frequencies bounded away from zero, the Landau damping of the density is
similar to the confined case. The finite regularity is possible due to an
additional dispersive mechanism available on $\mathbb R_x^3$ which reduces the
strength of the plasma echo resonance.
