  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 $1 < p <
+\infty$.
