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The Bohr radius of the unit ball of
-
Andreas Defant
and
Leonhard Frerick
Published/Copyright:
June 28, 2011
Abstract
By a classical result due to Aizenberg, Boas and Khavinson the Bohr radius 
of the unit ball in the Minkowski space 
, 1 ≦ p ≦ ∞, is up to an absolute constant ≦ (log n/n)1–1/min(p, 2). Our main result shows that this estimate is optimal. For p = ∞, this was recently proved in [Defant, Frerick, Ortega-Cerdà, Ounaies and Seip, Ann. Math. 174: 1–13, 2011] as a consequence of the hypercontractivity of the Bohnenblust–Hille inequality for polynomials. Using substantially different methods from local Banach space theory, we give a proof which covers the full scale 1 ≦ p ≦ ∞.
Received: 2010-02-12
Revised: 2010-08-11
Published Online: 2011-06-28
Published in Print: 2011-November
© Walter de Gruyter Berlin · New York 2011
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