Boundedness Theorems for Composition-Differentiation Operators Acting on Classical Function Spaces on Bidisk
DOI:
https://doi.org/10.30495/jme.v20i0.3709Abstract
We establish boundedness criteria for products of composition and differentiation operators acting from weighted Bergman space $ A^2_{\alpha_{1}, \alpha_{2} }(\mathbb{D}^2)$ on the bidisk into the weighted Bergman space $A^2_\beta(\mathbb{D})$ on the unit disk. We then derive sufficient conditions on the symbol functions to guarantee the boundedness of composition-differentiation operators acting from the Hardy space $H^2(\mathbb{D}^2)$ on the bidisk into the Hardy space $H^2(\mathbb{D})$ on the unit disk.
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