Weighted $L^p-$spaces on locally compact groups

Abstract

Let $G$ be a locally compact group, $\omega$ be a weight function on $G$ and $0<p<1$. We investigate the space $L^p(G,\omega){\star}L^p(G,\omega)$ as a subset of some special spaces such as $L^p(G,\omega)$, $L^{\infty}(G,1/\widetilde{\omega})$ and $C_0(G,1/\widetilde{\omega})$. As the main result we show that all of the mentioned inclusions are equivalent to the discreteness of $G$.