  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 $B$.
