On a class of pluriharmonic mappings in the unit polydisk

Sujoy Majumder; Goutam Haldar; Abhijit Banerjee; Shantanu Panja

On a class of pluriharmonic mappings in the unit polydisk

Complex Variables 2026-07-13 v1

Authors: Sujoy Majumder , Goutam Haldar , Abhijit Banerjee , Shantanu Panja

Abstract

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 $\mathcal{W}_{\mathcal{H}_n^0}(\alpha)$ .

Keywords

pluriharmonic mappings unit polydisk coefficient bounds growth estimates convex combination sections

Cite

@article{arxiv.2607.11629,
  title  = {On a class of pluriharmonic mappings in the unit polydisk},
  author = {Sujoy Majumder and Goutam Haldar and Abhijit Banerjee and Shantanu Panja},
  journal= {arXiv preprint arXiv:2607.11629},
  year   = {2026}
}