  Let $p(\cdot):\ \mathbb R^n\to(0,\infty)$ be a variable exponent function
satisfying the globally log-H\"older continuous condition. In this article, the
authors first obtain a decomposition for any distribution of the variable weak
Hardy space into "good" and "bad" parts and then prove the following real
interpolation theorem between the variable Hardy space $H^{p(\cdot)}(\mathbb
R^n)$ and the space $L^{\infty}(\mathbb R^n)$: \begin{equation*}
(H^{p(\cdot)}(\mathbb R^n),L^{\infty}(\mathbb R^n))_{\theta,\infty}
=W\!H^{p(\cdot)/(1-\theta)}(\mathbb R^n),\quad \theta\in(0,1), \end{equation*}
where $W\!H^{p(\cdot)/(1-\theta)}(\mathbb R^n)$ denotes the variable weak Hardy
space. As an application, the variable weak Hardy space
$W\!H^{p(\cdot)}(\mathbb R^n)$ with
$p_-:=\mathop\mathrm{ess\,inf}_{x\in\rn}p(x)\in(1,\infty)$ is proved to
coincide with the variable Lebesgue space $W\!L^{p(\cdot)}(\mathbb R^n)$.
