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Composition operators on Hardy-Orlicz spaces


About this Title

Pascal Lefèvre, Université d’Artois, Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P.\kern1mm 18, 307 LENS Cedex, France, Daniel Li, Université d’Artois, Laboratoire de Mathématiques de Lens EA 2462, Fédération CNRS Nord-Pas-de-Calais FR 2956, Faculté des Sciences Jean Perrin, Rue Jean Souvraz, S.P., 62 307 Lens Cedex, France, Hervé Queffélec, Université des Sciences et Technologies de Lille, Laboratoire Paul Painlevé U.M.R. CNRS 8524, U.F.R. de Mathématiques, 59 655 Villeneuve D’ascq Cedex, France and Luis Rodríguez-Piazza, Universidad de Sevilla, Facultad de Matemáticas, Dpto de Análisis Matemático, Apartado de Correos 1160, 41 080 Sevilla, Spain

Publication: Memoirs of the American Mathematical Society
Publication Year: 2010; Volume 207, Number 974
ISBNs: 978-0-8218-4637-7 (print); 978-1-4704-0588-5 (online)
DOI: http://dx.doi.org/10.1090/S0065-9266-10-00580-6
Published electronically: March 17, 2010
MathSciNet review: 2681410
Keywords:Bergman-Orlicz space, Carleson measure, composition operator, Hardy-Orlicz space
MSC: Primary 47B33; Secondary 30H10, 30H20, 46E15, 46E30

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Table of Contents


Chapters

  • Chapter 1. Introduction
  • Chapter 2. Notation
  • Chapter 3. Composition operators on Hardy-Orlicz spaces
  • Chapter 4. Carleson measures
  • Chapter 5. Bergman spaces

Abstract


We investigate composition operators on Hardy-Orlicz spaces when the Orlicz function grows rapidly: compactness, weak compactness, to be -summing, order bounded, …, and show how these notions behave according to the growth of . We introduce an adapted version of Carleson measure. We construct various examples showing that our results are essentially sharp. In the last part, we study the case of Bergman-Orlicz spaces.

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