  In this paper, we will discuss the space of functions of weak bounded mean
oscillation. In particular, we will show that this space is the dual space of
the special atom space, whose dual space was already known to be the space of
derivative of functions (in the sense of distribution) belonging to the Zygmund
class of functions. We show in particular that this proves that the Hardy space
$H^1$ strictly contains the space special atom space.
