The generalized Libera transform is bounded on the Besov mixed-norm, BMOA and VMOA spaces on the unit disc

The main results of this note prove that the generalized Libera operator is bounded on the Besov mixed-norm space Bαp,q(D) as well as on the spaces BMOA and VMOA   on the unit disk. The compactness of the operator on Bαp,q(D) is also studied.