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Weights, Extrapolation and the Theory of Rubio de Francia

  • Book
  • © 2011

Overview

Authors:
  1. David V. Cruz-Uribe

    1. , Department of Mathematics, Trinity College, Hartford, USA

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  2. José Maria Martell

    1. , Consejo Superior de Investigaciones Cien, Instituto de Ciencias Matemáticas, Madrid, Spain

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    You can also search for this author in PubMed   Google Scholar

  3. Carlos Pérez

    1. , Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

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  • No other book available devoted to the theory of extrapolation. Only treatment of extrapolation and factorization and its applications to two-weight norm inequalities
  • Introduction of new techniques for proving two-weight norm inequalities
  • Careful analysis of the proof of the classical extrapolation theorem of Rubio de Francia, demonstration of how the key ideas can be generalized to a wide variety of settings
  • Includes supplementary material: sn.pub/extras

Part of the book series: Operator Theory: Advances and Applications (OT, volume 215)

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Table of contents (10 chapters)

  1. Front Matter

    Pages i-xiii
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  2. One-Weight Extrapolation

    1. Front Matter

      Pages 1-1
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    2. Introduction to Norm Inequalities and Extrapolation

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 3-16

    3. The Essential Theorem

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 17-26

    4. Extrapolation for Muckenhoupt Bases

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 27-63

    5. Extrapolation on Function Spaces

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 65-93

  3. Two-Weight Factorization and Extrapolation

    1. Front Matter

      Pages 95-95
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    2. Preliminary Results

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 97-121

    3. Two-Weight Factorization

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 123-134

    4. Two-Weight Extrapolation

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 135-162

    5. Endpoint and A ∞ Extrapolation

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 163-174

    6. Applications of Two-Weight Extrapolation

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 175-200

    7. Further Applications of Two-Weight Extrapolation

      • David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 201-236

  4. Back Matter

    Pages 237-280
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Keywords

About this book

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 extrapolation theorem that fully develops the power of the Rubio de Francia iteration algorithm. This technique allows us to give a unified presentation of the theory and to give important generalizations to Banach function spaces and to two-weight inequalities. We provide many applications to the classical operators of harmonic analysis to illustrate our approach, giving new and simpler proofs of known results and proving new theorems. The book is intended for advanced graduate students and researchers in the area of weighted norm inequalities, as well as for mathematicians who want to apply extrapolation to other areas such as partial differential equations. 

Reviews

From the reviews:

The book is written with care and it will be attractive to readers with different interests. In particular, the short but general overview on weighted norm inequalities and extrapolation given in Chapter 1 should be appealing to a broad audience, and many analysts will find valuable the part dealing with one-weighted inequalities, while the necessarily more technical presentation of the two-weight theory demands better preparation from the reader.

Javier Duoandikoetxea (Mathematical Reviews)

“This book presents some recent aspects of weighted norm inequalities, in particular, it deals with generalizations and applications of the extrapolation theorem of Rubio de Francia. It is well-written and its contents are well-organized. … it is useful … not only for researchers and students who are working on weighted norm inequalities but also for mathematicians working in other areas of harmonic analysis.” (Yasuo Komori, Zentralblatt MATH, Vol. 1234, 2012)

Authors and Affiliations

  • , Department of Mathematics, Trinity College, Hartford, USA

    David V. Cruz-Uribe

  • , Consejo Superior de Investigaciones Cien, Instituto de Ciencias Matemáticas, Madrid, Spain

    José Maria Martell

  • , Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Carlos Pérez

Bibliographic Information

  • Book Title: Weights, Extrapolation and the Theory of Rubio de Francia

  • Authors: David V. Cruz-Uribe, José Maria Martell, Carlos Pérez

  • Series Title: Operator Theory: Advances and Applications

  • DOI: https://doi.org/10.1007/978-3-0348-0072-3

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel AG 2011

  • Hardcover ISBN: 978-3-0348-0071-6Published: 07 April 2011

  • Softcover ISBN: 978-3-0348-0328-1Published: 29 May 2013

  • eBook ISBN: 978-3-0348-0072-3Published: 06 April 2011

  • Series ISSN: 0255-0156

  • Series E-ISSN: 2296-4878

  • Edition Number: 1

  • Number of Pages: XIV, 282

  • Topics: Analysis

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