Estimating the norm of conformal maps in Korenblum-Orlicz spaces

Abstract

We use Young’s functions to define the Korenblum-Orlicz spaces as a generalization of the Korenblum spaces and we establish some of its properties. We show that the norm of the conformal maps in Korenblum-Orlicz spaces can be dominated by a certain expression involving the supremum over the inverse image of certain sectors. This extend a result of J. Ramos Fernandez in (C. R. Math. Acad. Sci. Paris, 344(5):291–294, 2007) for α-Bloch spaces.