On a class of pluriharmonic mappings in the unit polydisk

In this paper, we introduce and study the class ${\mathcal{W}}_{{\mathcal{H}}_n^0}(\alpha )$ of normalized pluriharmonic mappings, characterized by a suitable bound on their second-order partial derivatives. We establish a one-to-one correspondence between this pluriharmonic class and an associated class of holomorphic functions, thereby extending a result of Ghosh and Vasudevarao \cite{Ghosh-Allu-2019} to the setting of several complex variables. Furthermore, we obtain sharp coefficient bounds, growth estimates and a convex combination theorem for functions in ${\mathcal{W}}_{{\mathcal{H}}_n^0}(\alpha )$. Finally, we introduce sections (partial sums) of pluriharmonic mappings and investigate their properties for functions belonging to ${\mathcal{W}}_{{\mathcal{H}}_n^0}(\alpha )$.