We use the notion of radial derivative to introduce composition-differentiation operators on the Hardy and Bergman spaces of the unit ball and the polydisk. We seek for necessary and sufficient conditions on the inducing functions to ensure that the composition-differentiation operator is Hilbert-Schmidt.
Tent spaces and Littlewood-Paley $g$-functions associated with Bergman spaces in the unit ball of $\mathbb{C}^n$
Difference of Composition operators over Bergman spaces with exponential weights
Toeplitz operators on Bergman spaces of polygonal domains
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