Bohr phenomenon on the unit ball of a complex Banach space

Abstract

Let BX be the unit ball of a complex Banach space X . In this paper, we will generalize several results related to the Bohr radius for analytic functions or harmonic functions on the unit disc U in C to holomorphic mappings or pluriharmonic mappings on BX . We will establish Bohr’s inequality for the class of holomorphic mappings which are subordinate to convex mappings on BX . Next, we will establish Bohr’s inequality for pluriharmonic mappings on BX . We will also obtain the p -Bohr radius for bounded pluriharmonic functions on BX . Finally, we will determine the Bohr radius for a class of holomorphic functions on BX which contains odd holomorphic functions on BX . Mathematics subject classification (2010): 32A05, 32A10, 32K05.