Carleson measures on simply connected domains

Abstract: We study the Carleson measures associated to the Hardy and weighted Bergman spaces defined on general simply connected domains. This program was initiated by Zinsmeister in his paper \textit{Les domaines de Carleson }(1989), where he shows that the geometry of the domain plays a fundamental role. We will review the classical results presenting, in some cases, alternative proofs and will examine the situation for the weighted Bergman spaces.