the Littlewood-Paley $g$-function and $g_\lz^\ast$-function characterizations of $(HE_\Phi^q)_t(\rn)$ and also the finite atomic characterization.

We point out that, in [@af1], Ablé and Feuto introduced the Hardy-amalgam space $\mathcal{H}^{(p,q)}(\rn)$ and obtained the non-tangential maximal function characterization, the Poisson integral characterization and the atomic decomposition as well as the finite atomic decomposition of this space. To the best of our knowledge, this might be the first article to deal with the real-variable theory of Hardy spaces based on amalgam spaces. Comparing with [@af1], the approach used in this article via the general theory of [@ykds] for the corresponding characterizations of $(HE_\Phi^q)_t(\rn)$ is much simpler. Also, comparing with the atomic characterization of $\mathcal{H}^{(p,q)}(\rn)$ obtained in [@af1], the atomic characterization of $(HE_\Phi^q)_t(\rn)$ obtained in this article holds true on a wider range even when $(HE_\Phi^q)_t(\rn)$ is reduced to $\mathcal{H}^{(p,q)}(\rn)$ \[in this case, $t=1$ and $\Phi(\tau):=\tau^p$ for any $\tau\in [0,\fz)$ with $p\in (0,\fz)$\], which improves the related result in [@af1].

In Section \[s5\], as an application of both the atomic characterization (Theorem \[atom ch\]) and the finite atomic characterization (Theorem \[finite\]) of $(HE_\Phi^q)_t(\rn)$ obtained in Section \[s3\], we prove that the dual spaces of $(HE_\Phi^q)_t(\rn)$ can be described as certain Campanato spaces related to the 