有限原子线性组合空间的对偶性
Duality in spaces of finite linear combinations of atoms
摘要：
本文描述了$(p,\infty)$ -原子的有限线性组合空间$0<p\leq 1$ on ${\mathbb R}^n$的对偶和完备性.作为一个应用，我们给出了$(p,\infty)$ -原子上一致有界的算子的一个推广结果，即$0<p < 1$，它与$p=1$的类比是假的.设$0 < p <1$和$T$是定义在$(p,\infty)$ -原子的有限线性组合空间上的线性算子$0<p < 1 $，它取Banach空间$B$中的值.若$T$在$(p,\infty)$ -原子上一致有界，则$T$扩张为从$H^p({\mathbb R}^n)$到$B$的有界算子.
英文摘要：
In this note we describe the dual and the completion of the space of finite linear combinations of $(p,\infty)$-atoms, $0<p\leq 1$ on ${\mathbb R}^n$. As an application, we show an extension result for operators uniformly bounded on $(p,\infty)$-atoms, $0<p < 1$, whose analogue for $p=1$ is known to be false. Let $0 < p <1$ and let $T$ be a linear operator defined on the space of finite linear combinations of $(p,\infty)$-atoms, $0<p < 1 $, which takes values in a Banach space $B$. If $T$ is uniformly bounded on $(p,\infty)$-atoms, then $T$ extends to a bounded operator from $H^p({\mathbb R}^n)$ into $B$.
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