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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie

IMPACT FACTOR 2018: 1.859

CiteScore 2018: 1.14

SCImago Journal Rank (SJR) 2018: 2.554
Source Normalized Impact per Paper (SNIP) 2018: 1.411

Mathematical Citation Quotient (MCQ) 2018: 1.55

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Volume 2011, Issue 660


The Bohr radius of the unit ball of

Andreas Defant / Leonhard Frerick
Published Online: 2011-06-28 | DOI: https://doi.org/10.1515/crelle.2011.080


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 ≦ ∞.

About the article

Received: 2010-02-12

Revised: 2010-08-11

Published Online: 2011-06-28

Published in Print: 2011-11-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2011, Issue 660, Pages 131–147, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle.2011.080.

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