Geodesic
Composition operators on μ-Bloch spaces
Canadian journal of mathematics, Tome 61 (2009) no. 1, pp. 50-75

Voir la notice de l'article provenant de la source Cambridge University Press

Given a positive continuous function $\mu $ on the interval $0\,<\,t\,\le \,1$ , we consider the space of so-called $\mu $ -Bloch functions on the unit ball. If $\mu \left( t \right)\,=\,t$ , these are the classical Bloch functions. For $\mu $ , we define a metric $F_{z}^{\mu }\left( u \right)$ in terms of which we give a characterization of $\mu $ -Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao. 
Chen, Huaihui; Gauthier, Paul. Composition operators on μ-Bloch spaces. Canadian journal of mathematics, Tome 61 (2009) no. 1, pp. 50-75. doi: 10.4153/CJM-2009-003-1
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