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.

Detalhes bibliográficos
Autores: Bayart, F., Pellegrino, Daniel, Seoane Sepúlveda, Juan Benigno
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
Descrição
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.