论文标题
离散耐寒空间的分数系列操作员
Fractional series operators on discrete Hardy spaces
论文作者
论文摘要
我们估算$ h^{p}（\ mathbb {z}）$ - $ \ ell^{q}}（\ mathbb {z}）$分数系列操作员$t_γ$的界限\ [（t_γb）（t_γb）（j）= \ sum_ \ sum_ {i \ neq \ neq \ neq \ neq \ neq \ neq \ neq \ pm j} \ frac {b（i）} {| i -j |^α| i+ j |^β}，\]，其中$ 0 \ leqleqγ<1 $，$α，β> 0 $和$α+β= 1 -γ$。通过反示例，我们还表明，运算符$t_γ$不是从$ h^{p}（\ mathbb {z}）$限制到$ h^{q}（\ mathbb {z}）$。
We estudy the $H^{p}(\mathbb{Z})$ - $\ell^{q}(\mathbb{Z})$ boundedness of the fractional series operator $T_γ$ given by \[ (T_γb)(j) = \sum_{i \neq \pm j} \frac{b(i)}{|i-j|^α|i+j|^β}, \] where $0 \leq γ< 1$, $α, β> 0$ and $α+ β= 1 -γ$. By means of a counter-example, we also show that the operator $T_γ$ is not bounded from $H^{p}(\mathbb{Z})$ into $H^{q}(\mathbb{Z})$.
