Geodesic
Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2014), pp. 29-35 
Elke Wolf. Composition followed by differentiation between weighted Bergman spaces and weighted Banach spaces of holomorphic functions. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 2 (2014), pp. 29-35. http://geodesic.mathdoc.fr/item/BASM_2014_2_a3/
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     author = {Elke Wolf},
     title = {Composition followed by differentiation between weighted {Bergman} spaces and weighted {Banach} spaces of holomorphic functions},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
     pages = {29--35},
     year = {2014},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BASM_2014_2_a3/}
}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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