Weights, Extrapolation and the Theory of Rubio de Francia
This book provides a systematic development of the Rubio de Francia theory of extrapolation, its many generalizations and its applications to one and two-weight norm inequalities. The book is based upon a new and elementary proof of the classical ext
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Editors: Joseph A. Ball (Blacksburg, VA, USA) Harry Dym (Rehovot, Israel) Marinus A. Kaashoek (Amsterdam, The Netherlands) Heinz Langer (Vienna, Austria) Christiane Tretter (Bern, Switzerland) Associate Editors: Vadim Adamyan (Odessa, Ukraine) Albrecht Böttcher (Chemnitz, Germany) B. Malcolm Brown (Cardiff, UK) Raul Curto (Iowa, IA, USA) Fritz Gesztesy (Columbia, MO, USA) Pavel Kurasov (Lund, Sweden) Leonid E. Lerer (Haifa, Israel) Vern Paulsen (Houston, TX, USA) Mihai Putinar (Santa Barbara, CA, USA) Leiba Rodman (Williamsburg, VA, USA) Ilya M. Spitkovsky (Williamsburg, VA, USA)
Subseries Linear Operators and Linear Systems Subseries editors: Daniel Alpay (Beer Sheva, Israel) Birgit Jacob (Wuppertal, Germany) André C.M. Ran (Amsterdam, The Netherlands) Subseries Advances in Partial Differential Equations Subseries editors: Bert-Wolfgang Schulze (Potsdam, Germany) Michael Demuth (Clausthal, Germany) Jerome A. Goldstein (Memphis, TN, USA) Nobuyuki Tose (Yokohama, Japan) Ingo Witt (Göttingen, Germany)
Honorary and Advisory Editorial Board: Lewis A. Coburn (Buffalo, NY, USA) Ciprian Foias (College Station, TX, USA) J.William Helton (San Diego, CA, USA) Thomas Kailath (Stanford, CA, USA) Peter Lancaster (Calgary, Canada) Peter D. Lax (New York, NY, USA) Donald Sarason (Berkeley, CA, USA) Bernd Silbermann (Chemnitz, Germany) Harold Widom (Santa Cruz, CA, USA)
David V. Cruz-Uribe José Maria Martell Carlos Pérez
Weights, Extrapolation and the Theory of Rubio de Francia
Authors David V. Cruz-Uribe Department of Mathematics Trinity College 300 Summit Street Hartford, CT 06106-3100, USA [email protected]
José María Martell Instituto de Ciencias Matemáticas Consejo Superior de Investigaciones Científicas c/Serrano 121 28006 Madrid, Spain [email protected]
Carlos Pérez Departamento de Análisis Matemático Facultad de Matemáticas Universidad de Sevilla 41080 Sevilla, Spain [email protected]
2010 Mathematics Subject Classification: 42, 35, 46, 47
ISBN 978-3-0348-0071-6 e-ISBN 978-3-0348-0072-3 DOI 10.1007/978-3-0348-0072-3 Library of Congress Control Number: 2011926300 © Springer Basel AG 2011 This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in data banks. For any kind of use permission of the copyright owner must be obtained. Cover design: deblik, Berlin Printed on acid-free paper Springer Basel AG is part of Springer Science+Business Media www.birkhauser-science.com
Contents Preface
ix
Preliminaries
xi
I
1
One-Weight Extrapolation
1 Introduction to Norm Inequalities and 1.1 Weighted norm inequalities . . . 1.2 The theory of extrapolation . . . 1.3 The organization of this book . .
Extrapolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3 4 11 14
2 The Essential Theorem 2.1 The new proof . . . . .
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