On Stevic-Sharma operator from the Zygmund space to the Bloch-Orlicz space

Let D be the open unit disk in the complex plane C, phi an analytic self-map of D and H(D) the space of all analytic functions on D. In order to unify the products of composition, multiplication, and differentiation operators, Stevic and Sharma introduced the following so-called Stevic-Sharma operator: T(psi 1,psi 2,phi)f (z) = psi 1(z) f (phi(z)) + psi 2(z)f'(phi(z)), f is an element of H(D), where psi(1), psi(2) is an element of H(D). Here we characterize the boundedness and compactness of the operator T-psi 1,T-psi 2,T-phi from the Zygmund space to the Bloch-Orlicz space.