Multidimensional analogues of the improved Bohr's inequality for shifted polydisks

In this article, we investigate the Bhor phenomenon for holomorphic functions defined on a general simply connected domain in $\mathbb{C}^n$.

We improve the existing results Evdordis et al.

(Improved Bohr's inequality for shifted disks, Results in Mathematics, 76, 14 (2021)) for a broader class of holomorphic functions in $\mathbb{C}^n$.

Furthermore, we consider pluriharmonic mappings defined on a polydisk containing the unit polydisk $\mathbb{P}\Delta(0_n, 1_n)$ and establish a Bohr-type inequality for this class of mappings.