Weighted composition operators between weak spaces of vector-valued   analytic functions
  We consider weighted composition operators on spaces of analytic functions on the unit disc, which take values in some complex Banach space. We provide necessary and sufficient conditions for the boundedness and (weak) compactness of weighted composition operators on general function spaces, and in particular on weak vector-valued spaces. As an application, we characterize the weak compactness of these operators between two different vector-valued Bloch-type spaces. This result appears to be new also in the scalar-valued case. 
Mostafa Hassanlou, Jussi Laitila and Hamid Vaezi
math.FA