Composition operators on Hardy-Orlicz spaces

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 me...

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Bibliographic Details
Main Authors: Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé, Rodríguez-Piazza, Luis
Format: eBook Book
Language:English
Published: Providence, Rhode Island American Mathematical Society 2010
Edition:1
Series:Memoirs of the American Mathematical Society
Subjects:
Composition operators
Hardy spaces
composition operator
Bergman-Orlicz space
Carleson measure
Hardy-Orlicz space
ISBN:082184637X, 9780821846377
ISSN:0065-9266, 1947-6221
Online Access:Get full text
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Table of Contents:
  • Introduction -- Notation -- Composition operators on Hardy-Orlicz spaces -- Carleson measures -- Bergman spaces
  • Intro -- Contents -- Chapter 1. Introduction -- Chapter 2. Notation -- 1. Growth conditions -- 2. Some specific functions -- Chapter 3. Composition operators on Hardy-Orlicz spaces -- 1. Hardy-Orlicz spaces -- 2. Preliminary results -- 3. Composition operators -- 4. Order bounded composition operators -- 5. Weakly compact composition operators -- 6. p-summing operators -- Chapter 4. Carleson measures -- 1. Introduction -- 2. Compactness on H versus compactness on H2 -- 3. General measures -- 4. Characterization of the compactness of composition operators -- Chapter 5. Bergman spaces -- 1. Bergman-Orlicz spaces -- 2. Compact composition operators on Bergman-Orlicz spaces -- Acknowledgement -- References