Geodesic
On Bounded and Compact Composition Operators in Polydiscs
Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 869-889

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

Recently MacCluer and Shapiro [6] have characterized the compact composition operators in Hardy and weighted Bergman spaces of the disc, and MacCluer [5] has made an extensive study of these opertors in the unit ball of Cn. Angular derivatives and Carleson measures have played an essential role in these studies. In this article we study composition operators in poly discs and characterize those operators which are bounded or compact in Hardy and weighted Bergman spaces. In addition to Carleson measure theorems resembling those of [5], [6], we give necessary and sufficient conditions satisfied by the maps inducing bounded or compact composition operators. We conclude by considering the role of angular derivatives on the compactness question explicitly. 
Jafari, F. On Bounded and Compact Composition Operators in Polydiscs. Canadian journal of mathematics, Tome 42 (1990) no. 5, pp. 869-889. doi: 10.4153/CJM-1990-045-0
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