Orlicz spaces on hypergroups

For a locally compact hypergroup $K$ and a Young function $\varphi$, we study the Orlicz space $L^{\varphi}(K)$ and provide a sufficient condition for $L^{\varphi}(K)$ to be an algebra under convolution of functions. We show that a closed subspace of $L^\varphi(K)$ is a left ideal if and only if it is left translation invariant. We apply the basic theory developed here to characterize the space of multipliers of the Morse—Transue space $M^\varphi(K)$. We also investigate the multipliers of $L^\varphi(\mathcal{S},\pi_K)$, where $S$ is the support of the Plancherel measure $\pi_K$ associated to a commutative hypergroup $K$.