The Bohr-type inequalities for holomorphic functions with lacunary series in complex Banach space

2024/04/29 by Kumar, Shankey, Ponnusamy, Saminathan, Williams, G. Brock · 4 citations
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.18623

Abstract

In this paper, we study the Bohr inequality with lacunary series to the single valued (resp. vector-valued) holomorphic function defined in unit ball of finite dimensional Banach sequence space. Also, we extend the Bohr inequality with an alternating series to the higher-dimensional space.

Cited by

• Bohr inequalities for holomorphic mappings in higher-dimensional complex Banach spaces
• A Unified Study of Bohr's Inequality for analytic and harmonic mappings on the Unit Disk
• Estimates of the Second Bohr radius for vector-valued Holomorphic functions
• The Bohr inequality for vector-valued holomorphic functions with lacunary series in complex Banach spaces

Related

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