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

Sujoy Majumder; Goutam Haldar; Debabrata Pramanik; Shantanu Panja

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

Complex Variables 2026-07-12 v1

Authors: Sujoy Majumder , Goutam Haldar , Debabrata Pramanik , Shantanu Panja

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 $\mathcal{P}_{\mathcal{H}_n^0}(M)$ .

Keywords

pluriharmonic mappings coefficient bounds growth estimates unit polydisk several complex variables

Cite

@article{arxiv.2607.10616,
  title  = {Coefficient bounds and growth estimates for a class of pluriharmonic mappings in unit polydisk},
  author = {Sujoy Majumder and Goutam Haldar and Debabrata Pramanik and Shantanu Panja},
  journal= {arXiv preprint arXiv:2607.10616},
  year   = {2026}
}