# Composition operators on spaces of double Dirichlet series

## TL;DR

This paper investigates the properties of composition operators on spaces of double Dirichlet series, establishing their connections to holomorphic function spaces and characterizing superposition operators within these contexts.

## Contribution

It provides a new characterization of composition operators on spaces of double Dirichlet series and relates them to operators on holomorphic function spaces.

## Key findings

- Characterization of composition operators on bounded double Dirichlet series space
- Connection established between composition operators on Dirichlet series and holomorphic functions
- Superposition operators characterized on $ ext{H}^p$ spaces

## 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 $\HCdos$. 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 $\HC$ and in the spaces $\mathcal{H}^p$.