Bohr–Rogosinski radius for holomorphic mappings with values in higher dimensional complex Banach spaces

Abstract

In this paper, we investigate the Bohr–Rogosinski radius for holomorphic mappings on the unit ball of a complex Banach space with values in a higher dimensional complex Banach space. First, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit polydisc of the space \({\mathbb {C}}^n\), \(n\ge 2\). Next, we obtain the Bohr–Rogosinski radius for holomorphic mappings with values in the closure of the unit ball of a \(\hbox {JB}^*\)-triple. Finally, we obtain the Bohr–Rogosinski radius for a class of subordinations on the unit ball of a complex Banach space. All of the results are proved to be sharp.