A logarithmic lower bound for multi-dimensional bohr radii

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The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive (2009, unknown): “M ATHEMATIK , UNIVERSITÄT TRIER, D-54294 TRIER E-mail address: frerick@uni-trier.de”
Refined Bohr inequality for bounded analytic functions (2020, background): “r |z| = r ≤ √ 17− 3 4 . Besides these several authors have investigated some other extensions along with applications and connections with local Banach space theory and other topics. See for instance [2, 4, 8, 10, 11, 13, 14, 15, 16, 17, 18] and the references therein. In view of the recent developm”
Bohr’s theorem for holomorphic mappings with values in homogeneous balls (2009, unknown): “tion of Bohr’s theorem to several complex variables, see [2], [3], [4], [5], [ 9 ], [10], [11], [14], [19], [20] and [21].”