The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces

2025/08/26 by Ahammed, Sabir, Ahamed, Molla Basir, Hossain, Rajesh
#32A10 #32A22 #46E50 #46G25 #Complex Variables (math.CV) #FOS: Mathematics #Primary: 32A05 #Secondary: 46B20

paper · doi:10.48550/arxiv.2509.03532

Abstract

In this paper, we study the Bohr inequality with lacunary series for vector-valued holomorphic functions defined in unit ball of finite dimensional Banach sequence space. Also, we study the Bohr-Rogosinski inequality for same class of functions. All the results are proved to be sharp.

Citations

• Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces
• Multidimensional analogues of the refined versions of Bohr inequalities involving Schwarz mappings
• The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space
• Refined Bohr inequality for functions in ℂⁿ and in complex Banach spaces
• Bohr-type inequalities for unimodular bounded analytic functions
• Bohr-Rogosinski type inequalities for concave univalent functions
• Bohr radius for Banach spaces on simply connected domains
• Schwarz type lemmas and their applications in Banach spaces
• Bohr's Inequality for Non-commutative Hardy Spaces
• Generalization of Bohr-type inequality in analytic functions
• Note on Improved Bohr Inequality for harmonic mappings
• Modifications of Bohr's inequality in various settings
• The Bohr Phenomenon for analytic functions on simply connected domains
• Multidimensional analogues of refined Bohr's inequality
• Refined Bohr inequality for bounded analytic functions
• Bohr type inequalities for functions with a multiple zero at the origin
• Sharp Bohr type inequality
• Bohr's phenomenon for the classes of Quasi-subordination and K-quasiregular harmonic mappings
• Improved Bohr's phenomenon in quasi-subordination classes
• On the Bohr inequality with a fixed zero coefficient
• Mixed Bohr radius in several variables
• Improved Bohr's inequality for locally univalent harmonic mappings
• Bohr inequality for odd analytic functions
• Multidimensional analogues of Bohr's theorem on power series
• Bohr's power series theorem in several variables

Related

• The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space
• Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces
• Refined Bohr inequality for functions in ℂⁿ and in complex Banach spaces
• Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
• Multi-dimensional Bohr radii of Banach space valued holomorphic functions