Extensions of the Laurent Decomposition and the spaces $A^p(\Omega)$

TL;DR

This paper extends the Laurent decomposition to domains bounded by Jordan curves, explores the properties of the spaces $A^p( olinebreakig( olinebreakig) olinebreak)$, and investigates their relation to boundary function spaces, including non-Jordan domains.

Contribution

It generalizes the Laurent decomposition for more complex domains and analyzes the structure of the associated function spaces $A^p( olinebreakig( olinebreakig) olinebreak)$ and their boundary relations.

Findings

Generalized Laurent decomposition for Jordan curve domains

Characterized the spaces $A^p( olinebreakig( olinebreakig) olinebreak)$ and their boundary counterparts

Extended analysis to non-Jordan domains

Abstract

We generalize the classical Laurent decomposition in the setting of domains $\Omega\subseteq \mathbb C$ bounded by Jordan curves. This leads us to study the Fr\'echet spaces $A^p(\Omega)$, and their relation to the spaces $C^p(\partial \Omega)$. In the final section, we examine the case of a non Jordan domain $\Omega$.