generalized weighted composition operators acting between dirichlet-type spaces and bloch-type spaces

Let d = {υ ∈ c : |υ| < 1} be the open unit disk in the complex plane c and let h(d) be the space of all holomorphic functions on d. for a non-negative integer n and a function f ∈ h(d), the n th− order differentiation operator is defined as dnf = f (n). the weighted composition operator together with n th− order differentiation operator give rise to a new operator generally termed as generalized weighted composition operator denoted by wn ϕ,ξ and is defined by wn ϕ,ξf(υ) = ϕ(υ)f (n) (ξ(υ)), f ∈ h(d); υ ∈ d, where ϕ ∈ h(d) and ξ is a holomorphic self-map of d. this operator is basically the combination of multiplication operator mϕ, composition operator cξ and n th− order differentiation operator dn. we study the boundedness and compactness of this operator between dirichlet-type spaces and bloch-type spaces.