On multidimensional Bohr radius of finite dimensional Banach spaces

2025/06/30 by Vasudevarao Allu, Allu, Vasudevarao, Subhadip Pal +1
Mathematics · #32A05 #32A10 #46B07 #46G25 #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2506.23540

openalex publication_date 2025/06/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we improve the lower estimate of multidimensional Bohr radius for unit ball of ℓⁿ_q-spaces (1≤ q≤ ∞) for bounded holomorphic functions with values in finite dimensional complex Banach spaces. The new estimate provides the improved lower bound for the Bohr radius which was previously given by Defant, Maestre, and Schwarting [Adv. Math. 231 (2012), 2837--2857].

Citations

• Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces
• Multi-dimensional Bohr radii of Banach space valued holomorphic functions
• Bohr inequalities for free holomorphic functions on polyballs
• Majorant Series
• Multidimensional analogues of Bohr's theorem on power series
• Bohr's power series theorem in several variables

Related

• On multidimensional Bohr radii for Banach spaces
• Multidimensional Bohr radii for holomorphic functions with values in complex Banach spaces
• Asymptotic value of the multidimensional Bohr radius
• Estimates for generalized Bohr radii in one and higher dimensions
• Multi-dimensional Bohr radii of Banach space valued holomorphic functions