The nonlinear superposition operators between some analytic function spaces

Abstract

In this paper we characterize the nonlinear superposition operators mapping the space Q s \mathcal {Q}_s into the Dirichlet-type space D α p \mathcal {D}^p_\alpha and answer basically the remaining open cases provided by Galanopoulos, Girela, and Auxiliadora Márquez [J. Math. Anal. Appl. 463 (2018), pp. 659–680]. Meanwhile, we give some sufficient-necessary conditions for the superposition operators between Q s \mathcal {Q}_s spaces in all cases.