Bohrs power series theorem and local Banach space theory

DOI10.1515/crll.2003.030zbMath1031.46014OpenAlexW2009430575MaRDI QIDQ4415680

Domingo García, Manuel Maestre, Andreas Defant

Publication date: 6 August 2003

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/crll.2003.030

zbMATH Keywords

unconditional basisBanach-Mazur distanceBohr radiusBohr's inequalityGaussian random polynomial\(m\)-homogeneous polynomial

Mathematics Subject Classification ID

Gaussian processes (60G15) Local theory of Banach spaces (46B07) Probabilistic methods in Banach space theory (46B09) Power series, series of functions of several complex variables (32A05)

Related Items (44)

On Bohr radii of finite dimensional complex Banach spaces ⋮ Bohr and Rogosinski abscissas for ordinary Dirichlet series ⋮ Equivalent norms in polynomial spaces and applications ⋮ A decomposition theorem for polymeasures ⋮ A logarithmic lower bound for multi-dimensional Bohr radii ⋮ Bohr phenomena for Laplace-Beltrami operators ⋮ The \(p\)-Bohr radius of a Banach space ⋮ Bohr's theorem for holomorphic mappings with values in homogeneous balls ⋮ Estimates for the first and second Bohr radii of Reinhardt domains ⋮ Quantitative and qualitative estimates on the norm of products of polynomials ⋮ The Dirichlet–Bohr radius ⋮ On the Bohr Inequality ⋮ Sharp Bohr type inequality ⋮ Two generalizations of Bohr radius ⋮ Aspects of the Kahane-Salem-Zygmund inequalities in Banach spaces ⋮ A tensor norm preserving unconditionality for $\mathcal{L}_p$-spaces ⋮ Bohr and Rogosinski inequalities for operator valued holomorphic functions ⋮ Revisit of multi-dimensional Bohr radius ⋮ The Bohnenblust-Hille inequality for homogeneous polynomials is hypercontractive ⋮ The Bohr inequality in the hyperbolic plane ⋮ The Bohnenblust-Hille cycle of ideas from a modern point of view ⋮ A new approach towards estimating the \(n\)-dimensional Bohr radius ⋮ Sharp Bohr type real part estimates ⋮ Refined Bohr inequality for bounded analytic functions ⋮ Kahane-Salem-Zygmund polynomial inequalities via Rademacher processes ⋮ Remarks on the Bohr and Rogosinski phenomena for power series ⋮ Bohr's strips for Dirichlet series in Banach spaces ⋮ Bohr radii of vector valued holomorphic functions ⋮ Bohr's phenomenon for functions on the Boolean cube ⋮ Asymptotic estimates on the von Neumann inequality for homogeneous polynomials ⋮ Polynomial inequalities on the $\pi/4$-circle sector ⋮ Unconditionality for $m$-homogeneous polynomials on $\ell _{\infty }^{n}$ ⋮ Volume estimates in spaces of homogeneous polynomials ⋮ A new multilinear insight on Littlewood's 4/3-inequality ⋮ Convergence of Dirichlet polynomials in Banach spaces ⋮ Mixed Bohr radius in several variables ⋮ Bohr radius for classes of analytic functions ⋮ The Bohr inequality for holomorphic mappings with lacunary series in several complex variables ⋮ On unimodular multilinear forms with small norms on sequence spaces ⋮ Bohr phenomenon for operator-valued functions ⋮ Monomial convergence for holomorphic functions on \(\ell_r\) ⋮ Unconditional constants and polynomial inequalities ⋮ The Bohr inequality for Dirichlet series ⋮ Some generalizations of Bohr's theorem

Cites Work

• Cotype 2 estimates for spaces of polynomials on sequence spaces
• Summing inclusion maps between symmetric sequence spaces
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