  Let $A$ be an expansive dilation on $\mathbb{R}^n$, and
$p(\cdot):\mathbb{R}^n\rightarrow(0,\,\infty)$ be a variable exponent function
satisfying the globally log-H\"{o}lder continuous condition. Let
$\mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ be the variable anisotropic Hardy
space defined via the non-tangential grand maximal function. In this paper, the
authors obtain that the Fourier transform of $f\in
\mathcal{H}^{p(\cdot)}_A({\mathbb {R}}^n)$ coincides with a continuous function
$F$ on $\mathbb{R}^n$ in the sense of tempered distributions. As applications,
the authors further conclude a higher order convergence of the continuous
function $F$ at the origin and then give a variant of the Hardy-Littlewood
inequality in the setting of anisotropic Hardy spaces with variable exponents.
