Product-type operators on weak vector valued α-Besov spaces

Let psi(1) and psi(2) be analytic functions on the open unit disk D and phi an analytic self map on D. Let M-psi, C-phi and D denote the multiplication, composition and differentiation operators. We consider operators M psi 1C phi , M psi 2C phi D and the Stevic-Sharma operator T-psi 1,T-psi 2,T-phi(f) = M psi 1C phi(f)+M psi 2C phi D(f) on alpha-Besov space beta(p,alpha) and weak vector valued alpha-Besov space w beta(p,alpha)(X) for complex Banach space X and find some equivalent statements for boundedness of these operators. Also, boundedness and compactness of composition operator C-phi on beta(p,alpha)(D) and w beta(p,alpha)(D) are given.