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

Volume 80 / 2003

L. Aizenberg, E. Liflyand, A. Vidras Annales Polonici Mathematici 80 (2003), 47-54 MSC: Primary 42A05, 32A05; Secondary 32A07. DOI: 10.4064/ap80-0-3


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 $3\leq n\leq 10$.


  • L. AizenbergDepartment of Mathematics
    and Computer Science
    Bar-Ilan University
    52900 Ramat-Gan, Israel
  • E. LiflyandDepartment of Mathematics and Computer Science
    Bar-Ilan University, 52900 Ramat-Gan, Israel
  • A. VidrasDepartment of Mathematics and Statistics
    University of Cyprus
    Nicosia 1678, Cyprus

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