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DC Field | Value | Language |
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dc.contributor.author | Defant, Andreas | - |
dc.contributor.author | Frerick, Leonhard | - |
dc.contributor.author | Ortega Cerdà, Joaquim | - |
dc.contributor.author | Ounaïes, Myriam | - |
dc.contributor.author | Seip, Kristian | - |
dc.date.accessioned | 2013-03-22T12:26:18Z | - |
dc.date.available | 2013-03-22T12:26:18Z | - |
dc.date.issued | 2011 | - |
dc.identifier.issn | 0003-486X | - |
dc.identifier.uri | http://hdl.handle.net/2445/34364 | - |
dc.description.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 $\sqrt{N}\exp\{(-1/\sqrt{2}+o(1))\sqrt{\log N\log\log N}\}$. | - |
dc.format.extent | 13 p. | - |
dc.format.mimetype | application/pdf | - |
dc.language.iso | eng | - |
dc.publisher | Princeton University Press | - |
dc.relation.isformatof | Reproducció del document publicat a: http://dx.doi.org/10.4007/annals.2011.174.1.13 | - |
dc.relation.ispartof | Annals of Mathematics, 2011, vol. 174, num. 1, p. 485-497 | - |
dc.relation.uri | http://dx.doi.org/10.4007/annals.2011.174.1.13 | - |
dc.rights | (c) Annals of Mathematics, 2011 | - |
dc.source | Articles publicats en revistes (Matemàtiques i Informàtica) | - |
dc.subject.classification | Funcions de diverses variables complexes | - |
dc.subject.classification | Funcions holomorfes | - |
dc.subject.classification | Funcions de variables complexes | - |
dc.subject.other | Functions of several complex variables | - |
dc.subject.other | Holomorphic functions | - |
dc.subject.other | Functions of complex variables | - |
dc.title | The Bonenblust-Hille inequality for homogeneous polynomials is hypercontractive | - |
dc.type | info:eu-repo/semantics/article | - |
dc.type | info:eu-repo/semantics/publishedVersion | - |
dc.identifier.idgrec | 583199 | - |
dc.date.updated | 2013-03-22T12:26:18Z | - |
dc.rights.accessRights | info:eu-repo/semantics/openAccess | - |
Appears in Collections: | Articles publicats en revistes (Matemàtiques i Informàtica) |
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File | Description | Size | Format | |
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583199.pdf | 414.96 kB | Adobe PDF | View/Open |
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