Characterization of Hilbert-Schmidt Composition-Differentiation Operators Induced by Radial Derivative

We use the notion of radial derivative of analytic functions to introduce a new composition-differentiation operator on the classical spaces of analytic functions on the unit disk. These classical spaces of analytic functions include the Hardy space, the Bergman space, and the Dirichlet space. We then obtain necessary and sufficient conditions on the symbol function to ensure that the induced operator is Hilbert-Schmidt.

کلیدواژه ها:

composition operator ، Differentiation operator ، Hilbert-Schmidt operator ، Hardy space ، Bergman space ، Dirichlet space