Sequences of zeros of analytic function spaces and weighted superposition operators

Abstract

We use properties of the sequences of zeros of certain spaces of analytic functions in the unit disc $\mathbb{D}$ to study the question of characterizing the weighted superposition operators which map one of these spaces into another. We also prove that for a large class of Banach spaces of analytic functions in $\mathbb{D}$, $Y$, we have that if the superposition operator $S_{\phi }$ associated to the entire function $\phi$ is a bounded operator from $X$, a certain Banach space of analytic functions in $\mathbb{D}$, into $Y$, then the superposition operator $S_{{\phi }^{\prime }}$ maps $X$ into $Y$.

To appear in Monatshefte für Mathematik