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We give a simple characterization of chaos for weighted composition$C_0$-semigroups on $L^p_\rho(\Omega)$ for an open interval$\Omega\subseteq\mathbb{R}$. Moreover, we characterize chaos for these classesof $C_0$-semigroups on the closed subspace $W^{1,p}_*(\Omega)$ of the Sobolevspace $W^{1,p}(\Omega)$ for a bounded interval $\Omega\subset\mathbb{R}$. Thesecharacterizations simplify previously obtained characterization of chaos forthese classes of $C_0$-semigroups.

A simple characterization of chaos for weighted composition $C_0$-semigroups on Lebesgue and Sobolev spaces