Refined Bohr inequalities and a refined Bohr-Rogosinski inequality on complex Banach spaces

2024/09/25 by Molla Basir Ahamed, Ahamed, Molla Basir, Sabir Ahammed +3 · 2 citations
Computer Science · Mathematics · #Advanced Banach Space Theory #Complex Variables (math.CV) #FOS: Mathematics #Mathematical and Theoretical Analysis #Optimization and Variational Analysis

paper · pdf · doi:10.48550/arxiv.2409.16610

openalex publication_date 2024/09/25 · openalex created_date 2024/10/26 · openalex updated_date 2026/07/28

Abstract

In this paper, we first establish refined versions of the Bohr inequalities for the class of holomorphic functions from the unit ball B_X of a complex Banach space X into ℂ. As applications, we will establish refined Bohr inequalities of functional type or of norm type for holomorphic mappings with lacunary series on the unit ball B_X with values in higher dimensional spaces. Next, we obtain the Bohr-Rogosinski inequality for the class of holomorphic functions on B_X. In addition, we establish an improved version of the Bohr inequality for holomorphic functions on B_X. All the results are proved to be sharp.

Cited by

• Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces
• The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces

Related

• Refined Bohr inequality for functions in ℂⁿ and in complex Banach spaces
• Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
• The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces
• The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space
• Improved Bohr inequalities involving Fréchet derivatives associated with Holomorphic mappings in Banach spaces