Multidimensional analogue of the van der Corput–Visser inequality and its application to the estimation of the Bohr radius
Volume 80 / 2003
Annales Polonici Mathematici 80 (2003), 47-54
MSC: Primary 42A05, 32A05; Secondary 32A07.
DOI: 10.4064/ap80-0-3
Abstract
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 $ {\cal D}_1^n=\{z\in {\mathbb C}^n:\vert z_1\vert +\dots +\vert z_n\vert <1\}$ when $3\leq n\leq 10$.
