Bounded superposition operators between weighted Banach spaces of analytic functions

TL;DR

This paper characterizes entire functions that map between weighted Banach spaces of analytic functions via superposition, providing a comprehensive understanding of such transformations for general weights.

Contribution

It offers a complete characterization of superposition operators between weighted Banach spaces of analytic functions for broad classes of weights.

Findings

Identifies all entire functions inducing superposition operators between these spaces.

Provides conditions on weights for the boundedness of superposition operators.

Extends previous results to very general weight functions.

Abstract

We characterize all entire functions that transform a weighted Banach spaces of analytic functions $\mathcal{H}^{\infty}_{\mu_1}$ into another space of the same kind $\mathcal{H}^{\infty}_{\mu_2}$ by superposition for very general weights $\mu_1$ and $\mu_2$.