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

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 Fréchet 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 $\Omega$.

14 pages