$\mathcal{N}_p$-type functions with Hadamard gaps in the unit ball

TL;DR

This paper investigates the properties of holomorphic functions with Hadamard gaps within $ _p$-spaces on the unit ball in complex n-dimensional space, extending results to the unit disk.

Contribution

It provides new insights into the behavior of Hadamard gap functions in $ _p$-spaces for different ranges of p, including a corollary for the unit disk.

Findings

Characterization of Hadamard gap functions in $ _p$-spaces for $0<p eq n$

Extension of results from the unit ball to the unit disk

New corollary for analytic functions with Hadamard gaps on the disk

Abstract

We study the holomorphic functions with Hadamard gaps in $\mathcal{N}_p$-spaces on the unit ball of $\mathbb{C}^n$ when $0<p \le n$ and $p>n$. A corollary on analytic functions with Hadamard gaps on $\mathcal{N}_p$-spaces on the unit disk is also given.