Abstract:
Let $\phi$ be an analytic self-map of the open unit disk $\mathbb D$ in the complex plane. Such a map induces through composition a linear composition operator $C_\phi\colon f\mapsto f\circ\phi$. We are interested in the combination of $C_\phi$ weith the differentiation operator $D$, that is in the operator $DC_\phi\colon f\mapsto\phi'\cdot(f\circ\phi)$ acting between weighted Bergman spaces and weighted Banach spaces of holomorphic functions.
Keywords and phrases:composition operator, differentiation operator, weighted Bergman spaces, weighted Banach spaces of holomorphic functions.
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