论文标题
关于具有分布边界值的分析函数相关的矢量价值的注意事项
Note on vector valued Hardy spaces related to analytic functions having distributional boundary values
论文作者
论文摘要
在管域上定义的分析功能$ t^{c} \ subset \ mathbb {c}^{n} $，并在Banach space $ x $中取值，该$ x $已知具有$ x $ x $可值的分布边界值显示在硬质量$ h^{p}（p}（p}（p $ l^{p}（\ mathbb {r}^{n}，x）$，其中$ 1 \ leq p \ leq \ leq \ infty $和$ c $是常规的开放式凸锥。对于某些类别的Banach空间，包括反射性Banach的空间，还可以获得$ H^{p}（t^{c}，x）$元素的Poisson积分变换表示。
Analytic functions defined on a tube domain $T^{C}\subset \mathbb{C}^{n}$ and taking values in a Banach space $X$ which are known to have $X$-valued distributional boundary values are shown to be in the Hardy space $H^{p}(T^{C},X)$ if the boundary value is in the vector valued Lebesgue space $L^{p}(\mathbb{R}^{n},X)$, where $1\leq p \leq \infty$ and $C$ is a regular open convex cone. Poisson integral transform representations of elements of $H^{p}(T^{C}, X)$ are also obtained for certain classes of Banach spaces, including reflexive Banach spaces.
