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Let $G$ be a locally compact group, and let $1\le p < \infty$. Consider theweighted $L^p$-space $L^p(G,\omega)=\{f:\int|f\omega|^p<\infty\}$, where$\omega:G\to \mathbb R$ is a positive measurable function. Under appropriateconditions on $\omega$, $G$ acts on $L^p(G,\omega)$ by translations. When isthis action hypercyclic, that is, there is a function in this space such thatthe set of all its translations is dense in $L^p(G,\omega)$? H. Salas (1995)gave a criterion of hypercyclicity in the case $G=\mathbb Z$ . Under mildassumptions, we present a corresponding characterization for a general locallycompact group $G$. Our results are obtained in a more general setting when thetranslations only by a subset $S\subset G$ are considered.

Density of translates in weighted $L^p$ spaces on locally compact groups