Orlicz amalgam spaces and banach algebra structure

Let G be a locally compact group, Phi(1),Phi(2) be Young functions and omega be a moderate weight function on G. We introduce the weighted Orlicz amalgam spaces W(L-1(Phi)(G), L-2(Phi) (omega)(G)) defined on G, where the local component space is the Orlicz space L-1(Phi)(G) and the global component is the weighted Orlicz space L-2(Phi) (omega)(G). We derive some properties of the spaces W (L-1(Phi)(G), L-2(Phi) (omega) (G)) such as translation invariance, density and duality. We obtain an equivalent discrete type norm on W(L-1(Phi)(G), L-2(Phi) (omega)(G)). By using the equivalent norm, we characterize the Banach algebra W (L-1(Phi)(G), L-2(Phi) (omega)(G)) with respect to convolution when the underlying group is an IN group. We show that W (L-1(Phi)(G), L-2(Phi) (omega)(G)) admits no bounded approximate identity under certain conditions.