The Bohr radius of the $ n $-dimensional polydisk is equivalent to $\ sqrt {\ frac {\ log n}{n}} $
We show that the Bohr radius of the polydisk $\mathbb D^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential.
| Autores: | , , |
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| Tipo de documento: | artigo |
| Data de publicação: | 2014 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositório: | Docta Complutense |
| Idioma: | inglês |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/33847 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/33847 |
| Access Level: | Acceso aberto |
| Palavra-chave: | 51 Bohr radius Interpolation Bohnenblust–Hille inequality Matemáticas (Matemáticas) 12 Matemáticas |
| Resumo: | We show that the Bohr radius of the polydisk $\mathbb D^n$ behaves asymptotically as $\sqrt{(\log n)/n}$. Our argument is based on a new interpolative approach to the Bohnenblust--Hille inequalities which allows us to prove that the polynomial Bohnenblust--Hille inequality is subexponential. |
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