We study boundedness of weighted differentiation composition operators Dkφ,u between Zygmund type spaces Zα and Bloch type spaces β. We also give essential norm estimates of such operators in different cases of k  N and 0 < α,β < ∞. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

We give different types of new characterizations for the boundedness and essential norms of generalized weighted composition operators between Zygmund type spaces. Consequently, we obtain new characterizations for the compactness of such operators.

We consider weighted composition operators