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.

Detalles Bibliográficos
Autores: Bayart, F., Pellegrino, Daniel, Seoane Sepúlveda, Juan Benigno
Tipo de recurso: artículo
Fecha de publicación:2014
País:España
Institución:Universidad Complutense de Madrid (UCM)
Repositorio:Docta Complutense
Idioma:inglés
OAI Identifier:oai:docta.ucm.es:20.500.14352/33847
Acceso en línea:https://hdl.handle.net/20.500.14352/33847
Access Level:acceso abierto
Palabra clave:51
Bohr radius
Interpolation
Bohnenblust–Hille inequality
Matemáticas (Matemáticas)
12 Matemáticas
Descripción
Sumario: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.