Some applications of the dual spaces of Hardy-amalgam spaces

In this paper, thanks to the generalizations of the dual spaces of the Hardy-amalgam spaces ${\mathcal{H}}^{(q,p)}$ and ${\mathcal{H}}_{\mathrm{l}\mathrm{o}\mathrm{c}}^{(q,p)}$ for $0<q\le 1$ and $q\le p<\mathrm{\infty }$, 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 ${\mathcal{H}}_{\mathrm{l}\mathrm{o}\mathrm{c}}^{(q,p)}$ for $0<q\le 1$ and $q\le p<\mathrm{\infty }$. 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 $BMO({\mathbb{R}}^d)$.