Geodesic
Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions
Serdica Mathematical Journal, Tome 37 (2011) no. 4, pp. 341-352.

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Let f be an analytic self-map of the open unit disk D in the complex plane and y be an analytic map on D. Such maps induce a weighted composition operator followed by differentiation DCf, y acting between weighted Banach spaces of holomorphic functions. We characterize boundedness and compactness of such operators in terms of the involved weights as well as the functions f and y.
Keywords: Weighted Composition Operators, Weighted Banach Spaces, Holomorphic Functions, Differentiation 
@article{SMJ2_2011_37_4_a6,
     author = {Wolf, Elke},
     title = {Weighted composition followed by differentiation between weighted {Banach} spaces of holomorphic functions},
     journal = {Serdica Mathematical Journal},
     pages = {341--352},
     publisher = {mathdoc},
     volume = {37},
     number = {4},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SMJ2_2011_37_4_a6/}
}
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Wolf, Elke. Weighted composition followed by differentiation between weighted Banach spaces of holomorphic functions. Serdica Mathematical Journal, Tome 37 (2011) no. 4, pp. 341-352. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_4_a6/