We shall provide a brief account on new achievements in the study of composition and composition-differentiation operators acting on classical spaces of analytic functions on the unit disk, as well as on the polydisk and the unit ball. The emphasis is given to the Hardy space, the Bergman space, and the Dirichlet space on the unit disk in complex plane. In the last section, we shall provide some new results regarding the Hilbert-Schmidt operators in the setting of several complex variables.
Ali Abkar (Tue,) studied this question.