Multidimensional analogue of the van der Corput-Visser inequality and its application to the estimation of the Bohr radius
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 𝓓₁ⁿ = {z ∈ ℂⁿ: |z₁|+. .. +|zₙ| < 1} when 3 ≤ n ≤ 10.