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Let $G$ be a locally compact abelian group, $w$ be a weight on $G$ and let  be $\Phi$ a Young function. The weighted Orlicz space is a natural generalization of the classical weighted Lebesgue space $L^p_w(G), 1 \leq p\leq \infty$ and it is denoted by $L^\Phi_w(G)$. In this talk, firstly we investigate the inclusions between the weighted Orlicz spaces depending on Young function $\Phi$ and weight $w$. And we obtain some fundamental properties of $L^\Phi_w(G)$.
The main purpose of this talk is to nd necessary and sucient conditions for the Banach algebra structure of the weighted Orlicz space with respect to pointwise multiplication and convolution. Especially, we focused on the Banach algebra $L^\Phi_w(G)$ with respect to convolution and study some properties such as characterization of the maximal ideal space, semisimplicity and determining the closed ideals of the Banach algebra$L^\Phi_w(G)$.
The talk is based on my Ph.D. thesis (Istanbul University, Department of Mathematics, Advisor: Serap Oztop).