  In this article we define the Calder\'on-Hardy spaces with variable exponents
on $\mathbb{R}^{n}$, $\mathcal{H}^{p(.)}_{q, \gamma}(\mathbb{R}^{n})$, and we
show that for $m \in \mathbb{N}$ the operator $\Delta^{m}$ is a bijective
mapping from $\mathcal{H}^{p(.)}_{q, 2m}(\mathbb{R}^{n})$ onto
$H^{p(.)}(\mathbb{R}^{n})$.
