Composition operators on spaces of double Dirichlet series

Abstract

We study composition operators on spaces of double Dirichlet series, focusing our interest on the characterization of the composition operators of the space of bounded double Dirichlet series $${\mathcal {H}}^\infty ({\mathbb {C}}_+^2)$$ . We also show how the composition operators of this space of Dirichlet series are related to the composition operators of the corresponding spaces of holomorphic functions. Finally, we give a characterization of the superposition operators in $${\mathcal {H}}^\infty ({\mathbb {C}}_+)$$ and in the spaces $${\mathcal {H}}^p$$ .