Superposition operators between logarithmic Bloch spaces

Abstract

We characterize all entire functions $$\phi $$ that maps a logarithmic Bloch-type space $${\mathcal {B}}^\alpha _{\log ^\beta }$$ into another of the same kind by superposition. As consequences of our study, we obtain several results about the boundedness of superposition operators acting between $$\alpha $$ -Bloch spaces, Bloch–Orlicz spaces among others.