  In this paper, we study the asymptotic stability of Penrose-stable equilibria
among solutions of the screened Vlasov-Poisson system in $\mathbb{R}^d$ with
$d\geq 3$ that was first established by Bedrossian, Masmoudi, and Mouhot in
\cite{JBedrossian2018} with smooth initial data. More precisely, we prove the
sharp decay estimates for the density of the perturbed system, exactly like the
free transport with only H\"older (i.e., $C^{a}$ for $0<a<1$) perturbed initial
data. This improves the recent works in \cite{HanKwanD2021} by Han-Kwan,
Nguyen, and Rousset for lower derivatives of the density and in
\cite{NguyenTT2020} by T. Nguyen for higher derivatives with a logarithmic
correction in time. Furthermore, we establish new estimates and cancellations
of the kernel to the linearized problem to obtain this result. Moreover, we
also prove this result for the Vlasov-Poisson system in which the electric
field obeys a general nonlinear Poisson equation containing massless
electrons/ions case.
