Restricted Admissible Limit for Domains of Finite Type

TL;DR

This paper explores the boundary behavior of holomorphic functions in finite type domains, extending classical results and enhancing understanding of the Lindelöf principle in complex analysis.

Contribution

It generalizes Cirka's classical boundary behavior results to finite type domains and broadens the Lindelöf principle applicability beyond the unit ball.

Findings

Established boundary limits for holomorphic functions in finite type domains.

Extended classical boundary behavior theorems to more general domains.

Connected boundary behavior with the Lindelöf principle in complex analysis.

Abstract

We investigate the boundary behavior of holomorphic functions with respect to a family of curves in a domain of finite type. This work is a generalization of \u{C}irka's classical result on the unit ball and it supplements the result by Cima and Krantz on the Lindel\"{o}f principle for general domains. See [KRA2] for some recent developments in this subject