Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

Online
ISSN
1435-5345
See all formats and pricing
More options …
Volume 2011, Issue 660

Issues

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

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 ≦ ∞.

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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

[1]
Frédéric Bayart, Andreas Defant, and Sunke Schlüters
Journal d'Analyse Mathématique, 2019, Volume 138, Number 1, Page 107

Comments (0)

Please log in or register to comment.
Log in