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Let (a) :=(a1,...,an) ∈[1,∞)n,(p):=(p1,...,pn) ∈ (0,1]n,H(p)(a)(Rn)be the anisotropic mixed-norm Hardy space associated with (a) defined via the radial maximal function,and let f belong to the Hardy spaceH(p)(a)(Rn).In this article,we show that the Fourier transform 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 (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(p)(a)(Rn) 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 Rn.