标题： 分数级数算子在$\mathbb{Z}^n$上 显示英文标题

标题： Fractional series operators on $\mathbb{Z}^n$

摘要： 对于$0 \leq \alpha < n$和$m \in \mathbb{N} \cap (1 - \frac{\alpha}{n}, \, \infty)$，我们引入了一类在$\mathbb{Z}^n$上定义的分数级数算子$T_{\alpha, m}$，这些算子由具有整数系数的某些$m$-可逆矩阵生成。 在本文中，我们证明了$T_{\alpha, m}$是一个有界算子$H^p(\mathbb{Z}^n) \to \ell^q(\mathbb{Z}^n)$对于$0 < p < \frac{n}{\alpha}$和$\frac{1}{q} = \frac{1}{p} - \frac{\alpha}{n}$。 这推广了作者在[Acta Math. Hungar., 168 (1) (2022), 202-216]中获得的结果。 显示英文摘要

摘要： For $0 \leq \alpha < n$ and $m \in \mathbb{N} \cap (1 - \frac{\alpha}{n}, \, \infty)$, we introduce a class of fractional series operators $T_{\alpha, m}$ defined on $\mathbb{Z}^n$ which are generated by certain $m$-invertible matrices with integer coefficients. In this note, we prove that $T_{\alpha, m}$ is a bounded operator $H^p(\mathbb{Z}^n) \to \ell^q(\mathbb{Z}^n)$ for $0 < p < \frac{n}{\alpha}$ and $\frac{1}{q} = \frac{1}{p} - \frac{\alpha}{n}$. This generalizes the results obtained by the author in [Acta Math. Hungar., 168 (1) (2022), 202-216].