Some applications of the dual spaces of Hardy-amalgam spaces

Abstract

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

31 pages