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 $\mathbb{P}\mathrm{\Delta }(0_n,1_n)$ and establish a Bohr-type inequality for this class of mappings.