Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/34364
 Title: The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive Author: Defant, AndreasFrerick, LeonhardOrtega Cerdà, JoaquimOunaïes, MyriamSeip, Kristian Keywords: Funcions de diverses variables complexesFuncions holomorfesFuncions de variables complexesFunctions of several complex variablesHolomorphic functionsFunctions of complex variables Issue Date: 2011 Publisher: Princeton University Press Abstract: The Bohnenblust-Hille inequality says that the $\ell^{\frac{2m}{m+1}}$ -norm of the coefficients of an $m$-homogeneous polynomial $P$ on $\Bbb{C}^n$ is bounded by $\| P \|_\infty$ times a constant independent of $n$, where $\|\cdot \|_\infty$ denotes the supremum norm on the polydisc $\mathbb{D}^n$. The main result of this paper is that this inequality is hypercontractive, i.e., the constant can be taken to be $C^m$ for some $C>1$. Combining this improved version of the Bohnenblust-Hille inequality with other results, we obtain the following: The Bohr radius for the polydisc $\mathbb{D}^n$ behaves asymptotically as $\sqrt{(\log n)/n}$ modulo a factor bounded away from 0 and infinity, and the Sidon constant for the set of frequencies $\bigl\{ \log n: n \text{a positive integer} \le N\bigr\}$ is $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$. Note: Reproducció del document publicat a: http://dx.doi.org/10.4007/annals.2011.174.1.13 It is part of: Annals of Mathematics, 2011, vol. 174, num. 1, p. 485-497 URI: http://hdl.handle.net/2445/34364 Related resource: http://dx.doi.org/10.4007/annals.2011.174.1.13 ISSN: 0003-486X Appears in Collections: Articles publicats en revistes (Matemàtiques i Informàtica)

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