Weighted Lp-spaces on locally compact groups

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-infinity(G, 1/(omega) over tilde) and C-0(G, 1/(omega) over tilde). As the main result we show that all of the mentioned inclusions are equivalent to the discreteness of G.