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

Stability estimates for the Vlasov-Poisson system in $p$-kinetic Wasserstein distances