space, or between the Hardy-type space $(\mathfrak{C}_r^q)_t(\rn)$, with $t\in (0,\fz)$, $r\in (1,\fz)$ and $q\in (\frac n{n+1}, 1]$, from [@ap] and $(HE_\Phi^q)_t(\rn)$ in the case when $\Phi(\tau):=\tau^s$ for any $\tau\in [0,\fz)$ with $s\in (\frac n{n+1},q]$ are also clarified. All these results of this article are new even for slice Hardy spaces and, moreover, for Hardy-amalgam spaces, the molecular characterization, the Littlewood-Paley function characterizations, the dual spaces and the boundedness of $\delta$-type Calderón-Zygmund operators on these Hardy-type spaces are also new. Thus, the results obtained in this article essentially complement and generalize the real-variable theories of the Hardy-amalgam space in [@af1] as well as the Hardy-type space $H_*^\Phi(\rn)$ in [@bf].

To be more precise, in Section \[s2\] of this article, we introduce the notion of Orlicz-slice spaces $(E_\Phi^q)_t(\rn)$ and then present some basic properties of $(E_\Phi^q)_t(\rn)$, such as their equivalence relation with the Orlicz-amalgam spaces (see Proposition \[th2\] below), the Fefferman-Stein vector-valued inequality for the Hardy-Littlewood maximal operator on $(E_\Phi^q)_t(\rn)$ (see Theorem \[main\] below), the boundedness of the Hardy-Littlewood maximal operator on $(E_\Phi^q)_t(\rn)$ (see Corollary \[main2\] below), and the dual spaces of $(E_\Phi^q)_t(\rn)$ (see Theorem \[dual\] below). The boundedness of the Hardy-Littlewood maximal operator on $(E_\Phi^q)_t(\rn)$ is a key tool in this 