Weighted Composition-differentiation operators on weighted Dirichlet spaces

We study weighted composition-differentiation operators of order $n,$ $D^n_{ψ,φ}f:= ψ\cdot f^{(n)}\circ φ$ on weighted Dirichlet spaces. Our main goal is to describe the operator-theoretic properties of $D^n_{ψ,φ}$ in terms of the inducing functions $ψ$ and $φ.$ We characterize bounded, compact, and