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

摘要

We give a simple characterization of chaos for weighted composition$C_0$-semigroups on $L^p_ho(Omega)$ for an open interval$Omegasubseteqmathbb{R}$. 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 $Omegasubsetmathbb{R}$. Thesecharacterizations simplify previously obtained characterization of chaos forthese classes of $C_0$-semigroups.