Bohr's strips for Dirichlet series in Banach spaces
type: Item
instance of: scholarly article
title: Bohr's strips for Dirichlet series in Banach spaces
zbMATH Open document ID: 1227.30003
author: Andreas Defant
author: Domingo García
author: Manuel Maestre
author: Pablo Sevilla-Peris
published in: Functiones et Approximatio. Commentarii Mathematici
publication date: 2011-06-29T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.facm/1308749122
review text: The Bohr-Bohnenblust-Hille Theorem states that the width of the largest possible strip in \(\mathbb{C}\) on which any given ordinary Dirichlet series \(\sum_{n\geq 1}a_nn^{-s}\) (with variable \(s\in\mathbb{C}\) and coefficients \(a_n\in\mathbb{C}\)) converges uniformly but not absolutely is equal to \(\frac{1}{2}.\) Bohr-Bohnenblust-Hille's ideas led to improvements and to new nice results, in particular to Dirichlet polynomials or Dirichlet series with coefficients in Banach spaces. The paper gives a survey of various aspects of these developments as well as several open problems.
reviewed by: Augustin Mouze
Mathematics Subject Classification ID: 30B50
Mathematics Subject Classification ID: 46B07
Mathematics Subject Classification ID: 46B09
Mathematics Subject Classification ID: 46G20
zbMATH DE Number: 5914705
zbMATH Keywords: Dirichlet series
zbMATH Keywords: power series
zbMATH Keywords: polynomials
zbMATH Keywords: Banach spaces
MaRDI profile type: Publication
OpenAlex ID: W1965658507
cites work: The Bohr inequality for ordinary Dirichlet series
cites work: Inclusion mappings between \(l^p\) spaces
cites work: On the absolute convergence of Dirichlet series
cites work: Q4162061
cites work: Multilinear extensions of Grothendieck's theorem
cites work: Absolut-(p , 1)-summierende identische Operatoren von l u in l v
cites work: Quotient Algebras of Uniform Algebras
cites work: Sur l'ordre de grandeur des polynômes de Dirichlet
cites work: Unconditional basis and Gordon-Lewis constants for spaces of polynomials
cites work: Q4023934
cites work: The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive
cites work: Bohrs power series theorem and local Banach space theory
cites work: Bohr's strip for vector valued Dirichlet series
cites work: Bohr radii of vector valued holomorphic functions
cites work: Coordinatewise multiple summing operators in Banach spaces
cites work: Bohr's radii and strips -- a microscopic and a macroscopic view
cites work: A new multilinear insight on Littlewood's 4/3-inequality
cites work: Convergence of Dirichlet polynomials in Banach spaces
cites work: Q4850055
cites work: Q4257163
cites work: Q4076354
cites work: Some results in the metric theory of tensor products
cites work: The translation \(\frac 12\) in the theory of Dirichlet series
cites work: Some remarks on (p,q)-absolutely summing operators in $l_{p}$-spaces
cites work: Some remarks on the algebra of bounded Dirichlet series
cites work: Q4366920
cites work: H. Bohr's vision of ordinary Dirichlet series; old and new results
cites work: The best constant in the Khintchine inequality for complex Steinhaus variables, the case p=1
cites work: Cotype and \((q,1)\)-summing norm in a Banach space
cites work: Q4041061
cites work: Polarization and the two-dimensional Grothendieck inequality
DOI: 10.7169/FACM/1308749122
Recommended article: Bohr's strip for vector valued Dirichlet series
Recommended article: Algebras and Banach spaces of Dirichlet series with maximal Bohr's strip
Recommended article: On entire Dirichlet series bounded in a strip
Recommended article: Construction of an ordinary Dirichlet series with convergence beyond the Bohr strip
Recommended article: Some Banach spaces of Dirichlet series
Recommended article: Bohr's absolute convergence problem for \(\mathcal{H}_p\)-Dirichlet series in Banach spaces
Recommended article: On Bohr's theorem for general Dirichlet series
Recommended article: New strips of convergence for Dirichlet series
Recommended article: The Bohr inequality for Dirichlet series
Recommended article: The Bohr inequality for ordinary Dirichlet series
description: scientific article; zbMATH DE number 5914705