Boundedness of composition operators on some analytic function spaces

Abstract

In this paper, we investigate the necessary and sufficient conditions  for a composition operator $C_\phi$ to be bounded and compact from ${\cal B}_{\omega}^{\alpha}$ to $Q_{K,\omega}(p,q)$. Moreover, the necessary and sufficient condition for $C_{\phi}$ from the Dirichlet space $\mathcal{D}$ to the space $Q_{K, \omega}(p,q)$ to be compact is also given in terms of the map $\phi$.