LetD = {z ? C : |z| < 1} be the open unit disk in the complex plane C. By
H(D), denote the space of all holomorphic functions on D. For an analytic
self map ? on D and u, v ? H(D), we have a product type operator Tu,v,?
defined by Tu,v,? f (z) = u(z) f (?(z)) + v(z) f ?(?(z)), f ? H(D), z ? D,
This operator is basically a combination of three other operators namely
composition operator, multiplication operator and differentiation operator.
We study the boundedness and compactness of this operator from
Dirichlet-type spaces to Zygmund-type spaces.