Let \(B_k=\{x\in \mathbb R^n; |x|\leq 2^k\}\) and \(C_k=B_k \setminus B_{k-1}\) for \(k\in \mathbb Z\). Let \(\chi_k\) denote the characteristic function of the set \(C_k\). The homogeneous Herz space \(\dot K_q^{\alpha, p}(\mathbb R^n)\) is defined in terms of \[ \begin{aligned} \|f\|_{\dot K_q^{\alpha, p}(\mathbb R^n)}&=\bigl\{\sum_{k=-\infty}^\infty 2^{k\alpha p}\|f\chi_{k}\|_{L^q(\mathbb R^n)}^p\bigr\}^{1/p} \text{ by letting} \\ \dot K_q^{\alpha, p}(\mathbb R^n) &=\{f\in L_{\roman{loc}}^q(\mathbb R^n\setminus \{0\}); \|f\|_{\dot K_q^{\alpha, p}(\mathbb R^n)}<\infty\}.\end{aligned} \] The inhomogeneous Herz space \(K_q^{\alpha, p}(\mathbb R^n)\) is defined in terms of \[ \begin{aligned}\|f\|_{K_q^{\alpha, p}(\mathbb R^n)} &= \|f\chi_{B_0}\|_{L^q(\mathbb R^n)^p} +\bigl\{\sum_{k=1}^\infty 2^{k\alpha p}\|f\chi_{k}\|_{L^q(\mathbb R^n)}^p\bigr\}^{1/p} \text{ by letting} \\ K_q^{\alpha, p}(\mathbb R^n) &=\{f\in L_{\roman{loc}}^q(\mathbb R^n); \|f\|_{K_q^{\alpha, p}(\mathbb R^n)}<\infty\}, \\ \dot K_q^{0, q}(\mathbb R^n)&= L^q(\mathbb R^n)\text{ and} \\ \dot K_q^{\alpha/q, q}(\mathbb R^n)&=L_{|x|^\alpha}(\mathbb R^n).\end{aligned} \] Herz-type Hardy spaces are defined in terms of the grand maximal functions or radial maximal functions of distributions \(f\ast \varphi_t\) \((\varphi\in C_0^\infty(\mathbb R^n)\) with \(\int \varphi dx=1)\), normed by \(\dot K_q^{\alpha, p}(\mathbb R^n)\) or \(K_q^{\alpha, p}(\mathbb R^n)\), like as in the classical Hardy spaces. In most of the papers dealing with the Herz-type Hardy spaces, the studies are restricted to the case \(1