REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES

doi:10.1007/s10473-026-0102-9

Abstract

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 $\mathbb{C}$. 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.

Key words: Banach spaces, Bohr inequality, Bohr-Rogosinski inequality, homogeneous polynomial expansion, Lacunary series

CLC Number:

32A05

Molla Basir AHAMED¹, Sabir AHAMMED¹, Hidetaka HAMADA^2,*. REFINED BOHR INEQUALITIES AND A REFINED BOHR-ROGOSINSKI INEQUALITY ON COMPLEX BANACH SPACES[J].Acta mathematica scientia,Series B, 2026, 46(1): 19-38.

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