*Orlicz-amalgam space* $\ell^q(L^\Phi_t)(\rn)$ is defined to be the set of all measurable functions $f$ such that $$\|f\|_{\ell^q(L^\Phi_t)(\rn)}:=\lf[\sum_{k\in \mathbb{Z}^n}\lf\|f\chi_{Q_{tk}}\r\|^q_{L^\Phi(\rn)}\r]^{\frac{1}{q}}<\infty,$$ where $Q_{tk}:=t[k+[0,1)^n]$ for any $t\in(0,\infty)$ and $k\in\mathbb{Z}^n$.

\[re2.10\]

-   Both the Orlicz-slice space and the Orlicz-amalgam space fall into the scale of Wiener-amalgam spaces introduced by Feichtinger [@f]. By Lemmas \[lem1\], \[lem3\] and [@f Theorem 1], we know that both the Orlicz-slice space and the Orlicz-amalgam space are quasi-Banach spaces.

-   If $t=1$ and $\Phi(\tau):=\tau^p$ for any $\tau\in [0,\fz)$ with $p\in (0,\fz)$, then $(E_\Phi^q)_t(\rn)$ coincides with the Weiner amalgam spaces $(L^p,\ell^q)(\rn)$ in [@af1]. By [@af1 Proposition 2.1], we have $(L^p,\ell^q)(\rn)\subset L^p(\rn)\bigcap L^q(\rn)$ when $p\in(0, q)$ and $L^p(\rn)\bigcup L^q(\rn)\subset(L^p,\ell^q)(\rn)$ when $ q\in(0, p)$, here and hereafter, for any $r\in(0,\infty]$, the *symbol* $L^r(\rn)$ denotes the set of all measurable functions $f$ such that $$\|f\|_{L^r(\rn)}:=\lf\{\int_{\rn}|f(x)|^r\,dx\r\}^{1/r}<\infty$$ with the usual modification made when $r=\infty$.

-   If $\Phi(\tau):=\tau^r$ for any $\tau\in[0,\fz)$ with $r\in(0,\fz)$, then $(E_\Phi^q)_t(\rn)$ and $(E_r^q)_t(\rn)$ from [@am; @ap] coincide with equivalent quasi-norms.

The following proposition clarifies the relation between $(E_r^q)_t(\rn)$, with $t,\ q,\ r\in(0,\infty)$, and $L^q(\rn)$, whose proof is a slight modification of the proof of [@af1 Proposition 2.1].

\[ggg\] Let $t,\ q,\ r\in(0,\infty)$.

-   If $r\in(0, q]$, then $L^r(\rn)\cup L^q(\rn)\subset (E_r^q)_t(\rn)$; precisely, for any $f\in 