Coefficient bounds and growth estimates for a class of pluriharmonic mappings in unit polydisk

Abstract

In this paper, we first introduce and study the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$ of normalized pluriharmonic mappings, characterized by a specific bound on the sum of their second-order partial derivatives. We prove a one-to-one correspondence between this pluriharmonic class and a class of holomorphic functions, extending the known result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2020} to the setting of several complex variables. Finally, we provide sharp coefficient bounds and growth estimates for functions in the class $\mathcal{P}_{\mathcal{H}_n^0}(M)$.