  In this paper, thanks to the generalizations of the dual spaces of the
Hardy-amalgam spaces $\mathcal H^{(q,p)}$ and
$\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ for $0<q\leq1$ and $q\leq p<\infty$,
obtained in our earlier paper, we prove that the inclusion of $\mathcal
H^{(1,p)}$ in $(L^1,\ell^p)$ for $1\leq p<\infty$ is strict, and more
generally, the one of $\mathcal H^{(q,p)}$ in
$\mathcal{H}_{\mathrm{loc}}^{(q,p)}$ for $0<q\leq1$ and $q\leq p<\infty$.
Moreover, as other applications, we obtain results of boundedness of
Calder\'on-Zygmund and convolution operators, generalizing those known in the
context of the spaces $\mathcal H^1$ and $BMO(\mathbb{R}^d)$.
