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Archiv der Mathematik

, Volume 98, Issue 4, pp 327–340 | Cite as

Essential norm of composition operators on the Hardy space H 1 and the weighted Bergman spaces \({A_{\alpha}^{p}}\) on the ball

  • Stéphane Charpentier
Article

Abstract

We estimate the essential norm of a composition operator acting on the Hardy space H 1 and the weighted Bergman spaces \({A_{\alpha}^{p}}\) on the unit ball. In passing, we recover (and somehow simplify the proof of) parts of the recent article by Demazeux, dealing with the same question for H 1 of the unit disc. We also estimate the essential norm of a composition operator acting on \({A_{\alpha}^{p}}\) in terms of the angular derivatives of \({\phi}\), under a mild condition on \({\phi}\).

Mathematics Subject Classification (2010)

Primary 47B33 Secondary 32A36 

Keywords

Angular derivative Carleson measure Composition operator Essential norm Hardy space Several complex variables Weighted Bergman space 

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Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Laboratoire Paul Painlevé, UMR CNRS 8524Université Lille 1Villeneuve d’Ascq CedexFrance

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