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Due to the dissipative structure of \textit{regularity-loss}, extra higherregularity than that for the global-in-time existence is usually imposed toobtain the optimal decay rates of classical solutions to dissipative systems.The aim of this paper is to seek the lowest regularity index for the optimaldecay rate of $L^{1}(\mathbb{R}^n)$-$L^2(\mathbb{R}^n)$. Consequently, a notionof minimal decay regularity for dissipative systems of regularity-loss isfirstly proposed. To do this, we develop a new time-decay estimate of$L^p(\mathbb{R}^n)$-$L^{q}(\mathbb{R}^n)$-$L^{r}(\mathbb{R}^n)$ type by usingthe low frequency and high-frequency analysis in Fourier spaces. As anapplication, for compressible Euler-Maxwell equations with the weakerdissipative mechanism, it is shown that the minimal decay regularity coincideswith the critical regularity for global classical solutions. Moreover, therecent decay property for symmetric hyperbolic systems with non-symmetricdissipation is also extended to be the $L^p$-version.

$L^p$-$L^{q}$-$L^{r}$ estimates and minimal decay regularity for compressible Euler-Maxwell equations