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

Abstract

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 classes of $C_0$-semigroups on the closed subspace $W^{1,p}_*(\Omega)$ of the Sobolev space $W^{1,p}(\Omega)$ for a bounded interval $\Omega\subset\mathbb{R}$. These characterizations simplify previously obtained characterization of chaos for these classes of $C_0$-semigroups.