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Composition Operators on Hardy-Orlicz Spaces
Pascal Lefèvre and Daniel Li, Université d'Artois, Lens, France, Hervé Queffélec, Université des Sciences et Technologies de Lille, Villeneuve d'Ascq, France, and Luis Rodríguez-Piazza, Universidad de Sevilla, Spain
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Memoirs of the American Mathematical Society
2010; 74 pp; softcover
Volume: 207
ISBN-10: 0-8218-4637-X
ISBN-13: 978-0-8218-4637-7
List Price: US$64
Individual Members: US$38.40
Institutional Members: US$51.20
Order Code: MEMO/207/974
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The authors investigate composition operators on Hardy-Orlicz spaces when the Orlicz function \(\Psi\) grows rapidly: compactness, weak compactness, to be \(p\)-summing, order bounded, \(\ldots\), and show how these notions behave according to the growth of \(\Psi\). They introduce an adapted version of Carleson measure. They construct various examples showing that their results are essentially sharp. In the last part, they study the case of Bergman-Orlicz spaces.

Table of Contents

  • Introduction
  • Notation
  • Composition operators on Hardy-Orlicz spaces
  • Carleson measures
  • Bergman spaces
  • References
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