Some Necessary and Sufficient Conditions for Convolution Weighted Orlicz Algebras

In this paper, we give some sufficient conditions for a weighted Orlicz space L Φ w (G) to be a convolution Banach algebra, where G is a locally compact group and Φ is a Young function. Also, we prove a hereditary property regarding the discrete subgroups of G. Furthermore, we show that if G be an abelian locally compact group with an open compact subgroup, (Φ, Ψ) be a complementary pair of N-functions, and L Φ w (G) be a convolution Banach algebra, then 1/w∗ ∈ L Ψ (G).