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On Bounded and Compact Composition Operators in Polydiscs

Published online by Cambridge University Press:  20 November 2018

F. Jafari
F. Jafari*
Affiliation:
Bowdoin College, Department of Mathematics, Brunswick, Maine 04011, U. S. A.
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 42 , Issue 5 , 01 October 1990 , pp. 869 - 889
Copyright
Copyright © Canadian Mathematical Society 1990

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