Generalized versions of Lipschitz conditions on the modulus of holomorphic functions

TL;DR

This paper extends Lipschitz conditions to the norms of holomorphic functions between unit balls in complex spaces, broadening previous results and providing new insights into their behavior in complex analysis.

Contribution

It introduces generalized Lipschitz conditions for holomorphic mappings in higher-dimensional complex spaces, expanding upon prior work by Djordjević and Pavlović.

Findings

Established new Lipschitz bounds for holomorphic functions in complex spaces

Extended previous results to higher dimensions and more general spaces

Provided theoretical framework for analyzing holomorphic mappings

Abstract

In this paper, we establish Lipschitz conditions for the norm of holomorphic mappings between the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$ and $X,$ a complex normed space. This extends the work of Djordjevi\'{c} and Pavlovi\'{c}.