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We present a multidimensional analogue of an inequality by van der Corput–Visser concerning the coefficients of a real trigonometric polynomial. As an application, we obtain an improved estimate from below of the Bohr radius for the hypercone D 1 = {z ∈ C : |z1|+ . . .+ |zn| < 1} when 3 ≤ n ≤ 10. 1. Bohr radius. The following classical result can be found in [9]: If the power series ∞ ∑

Multidimensional analogue of the van der Corput–Visser inequality and its application to the estimation of the Bohr radius