Let $$\overrightarrow a \,: = \,\left( {{a_1}, \ldots,{a_n}} \right) \in {\left[ {1,\infty } \right)^n},\,\overrightarrow {p\,}: = \left( {{p_1}, \ldots,{p_n}} \right) \in {\left( {0,1} \right]^n},H_{\overrightarrow a }^{\overrightarrow p }\left( {{\mathbb{R}^n}} \right)$$ be the anisotropic mixed-norm Hardy space associated with $$\overrightarrow a $$ defined via the radial maximal function, and let f belong to the Hardy space $$H_{\overrightarrow a }^{\overrightarrow p }\left( {{\mathbb{R}^n}} \right)$$ . In this article, we show that the Fourier transform $$\widehat{f}$$ coincides with a continuous function g on ℝn in the sense of tempered distributions and, moreover, this continuous function g, multiplied by a step function associated with $$\overrightarrow a $$ , can be pointwisely controlled by a constant multiple of the Hardy space norm of f. These proofs are achieved via the known atomic characterization of $$H_{\overrightarrow a }^{\overrightarrow p }\left( {{\mathbb{R}^n}} \right)$$ and the establishment of two uniform estimates on anisotropic mixed-norm atoms. As applications, we also conclude a higher order convergence of the continuous function g at the origin. Finally, a variant of the Hardy-Littlewood inequality in the anisotropic mixed-norm Hardy space setting is also obtained. All these results are a natural generalization of the well-known corresponding conclusions of the classical Hardy spaces Hp(ℝn) with p ∈ (0, 1], and are even new for isotropic mixed-norm Hardy spaces on ∈n.