Surjective and closed range differentiation operator

We identify Fock-type spaces F(m,p) F ( m , p ) on which the differentiation operator D has closed range. We prove that D has closed range only if it is surjective, and this happens if and only if $$m=1$$ m = 1 . Moreover, since the operator is unbounded on the classical Fock spaces, we consider the modified or the weighted composition–differentiation operator, D(u,ψ ,n) f= u· ( f⁽ⁿ⁾∘ ψ ) D ( u , ψ , n ) f = u · ( f ( n ) ∘ ψ ) , on these spaces and describe conditions under which the operator admits closed range, surjective, and order bounded structures.