  In this paper, for a locally compact commutative hypergroup $K$ and for a
pair $(\Phi_1, \Phi_2)$ of Young functions satisfying sequence condition, we
give a necessary condition in terms of aperiodic elements of the center of $K,$
for the convolution $f\ast g$ to exist a.e., where $f$ and $g$ are arbitrary
elements of Orlicz spaces $L^{\Phi_1}(K)$ and $L^{\Phi_2}(K)$, respectively. As
an application, we present some equivalent conditions for compactness of a
compactly generated locally compact abelian group. Moreover, we also
characterize compact convolution operators from $L^1_w(K)$ into $L^\Phi_w(K)$.
