A Primer, and Beyond, on Composition Operators on the Unit Disk (New Mathematical Monographs)

Pascal Lefèvre , Hervé Queffélec

ISBN 10: 1009388894 / ISBN 13: 9781009388894

Published by Cambridge University Press, 2026

About this Item

2026. hardcover. . . . . . Books ship from the US and Ireland.

Seller Inventory # V9781009388894

Bibliographic Details

• Title: A Primer, and Beyond, on Composition Operators on the Unit Disk (New Mathematical Monographs)
• Publisher: Cambridge University Press
• Publication Date: 2026
• Language: English
• ISBN 10: 1009388894
• ISBN 13: 9781009388894
• Binding: Hardcover
• Condition: New

About this title

Synopsis

This is a contemporary treatment of composition operators on Banach spaces of analytic functions in one complex variable. It provides a step-by-step introduction, starting with a review (including full proofs) of the key tools needed, and building the theory with a focus on Hardy and Bergman spaces. Several proofs of operator boundedness (Littlewood's principle) are given, and the authors discuss approaches to compactness issues and essential norm estimates (Shapiro's theorem) using different tools such as Carleson measures and Nevanlinna counting functions. Membership of composition operators in various ideal classes (Schatten classes for instance) and their singular numbers are studied. This framework is extended to Hardy-Orlicz and Bergman-Orlicz spaces and finally, weighted Hardy spaces are introduced, with a full characterization of those weights for which all composition operators are bounded. This will be a valuable resource for researchers and graduate students working in functional analysis, operator theory, or complex analysis.

About the Authors

Pascal Lefèvre is a Professor at the University of Artois (France). After a Ph.D. thesis on harmonic analysis, Banach spaces and interplay with basic number theory he has worked for twenty years on composition operators.

Hervé Queffélec is an Emeritus Professor at the University of Lille (France). He completed his Ph.D. thesis on harmonic analysis, Banach spaces and Dirichlet series and has worked on composition operators for the last twenty-five years.