Bounded superposition operators between weighted Banach spaces of   analytic functions
  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 $\mu_2$. 
Julio C. Ramos-Fern\'andez
math.CV