We extend Loeper's L^2-estimate relating the electric fields to the densities for the Vlasov-Poisson system to L^p, with 1 < p < +\infty, based on the Helmholtz-Weyl decomposition. This allows us to generalize both the classical Loeper's 2-Wasserstein stability estimate and the recent stability estimate by the first author relying on the newly introduced kinetic Wasserstein distance to kinetic Wasserstein distances of order 1 < p < +\infty.
