the Littlewood-Paley function characterizations, the dual spaces and the boundedness of $\delta$-type Calderón-Zygmund operators on these Hardy-type spaces are also new. ]{}

Introduction\[s1\]
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The Hardy spaces $H^p(\rn)$, with $p\in (0, 1]$, are known to be one of the most important working spaces on $\rn$ in harmonic analysis and partial differential equations, which play key roles in many branches of analysis; see, for example, [@fs72; @fs82; @sto89; @em; @m94]. In particular, $H^p(\rn)$, with $p\in (0, 1]$, are good substitutes of Lebesgue spaces $L^p(\rn)$ when studying the boundedness of Calderón-Zygmund operators. In recent decades, in order to meet the requirements arising in the study of the boundedness of operators, partial differential equations and some other fields, various variants of Hardy spaces have been introduced and developed, such as weak Hardy spaces (see, for example, [@frs74; @fs87]), Hardy-Lorentz spaces (see, for example, [@at07; @abr17; @lyy16; @lyy17; @lyy18]) and Orlicz-Hardy spaces (see, for example, [@l66; @l67; @sto76; @yll]). Recently, in [@af1], as a generalization of the classical Hardy space and the Lorentz-Hardy space, Ablé and Feuto introduced the Hardy type space $\mathcal{H}^{(p,q)}(\rn)$ with $p,\,q\in(0,\infty)$ based on the N. Weiner amalgam spaces $(L^p,\ell^q)(\rn)$ and obtained an atomic decomposition of these Hardy-amalgam spaces when $q\in(0,\fz)$ 