  Let $\vec{p}\in(0,1]^n$ be a $n$-dimensional vector and $A$ a dilation. Let
$H_A^{\vec{p}}(\mathbb{R}^n)$ denote the anisotropic mixed-norm Hardy space
defined via the radial maximal function. Using the known atomic
characterization of $H_{A}^{\vec{p}}(\mathbb{R}^n)$ and establishing a uniform
estimate for corresponding atoms, the authors prove that the Fourier transform
of $f\in H_A^{\vec{p}}(\mathbb{R}^n)$ coincides with a continuous function $F$
on $\mathbb{R}^n$ in the sense of tempered distributions. Moreover, the
function $F$ can be controlled pointwisely by the product of the Hardy space
norm of $f$ and a step function with respect to the transpose matrix of $A$. As
applications, the authors obtain a higher order of convergence for the function
$F$ at the origin, and an analogue of Hardy--Littlewood inequalities in the
present setting of $H_A^{\vec{p}}(\mathbb{R}^n)$.
