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© 2011

Weights, Extrapolation and the Theory of Rubio de Francia

Book

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

Table of contents

  1. Front Matter
    Pages i-xiii
  2. One-Weight Extrapolation

    1. Front Matter
      Pages 1-1
    2. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 3-16
    3. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 17-26
    4. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 27-63
    5. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 65-93
  3. Two-Weight Factorization and Extrapolation

    1. Front Matter
      Pages 95-95
    2. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 97-121
    3. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 123-134
    4. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 135-162
    5. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 163-174
    6. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 175-200
    7. David V. Cruz-Uribe, José María Martell, Carlos Pérez
      Pages 201-236
  4. Back Matter
    Pages 237-280

About this book

Introduction

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. 

Keywords

Rubio de Francia extrapolation theorem harmonic analysis

Authors and affiliations

  1. 1., Department of MathematicsTrinity CollegeHartfordUSA
  2. 2., Consejo Superior de Investigaciones CienInstituto de Ciencias MatemáticasMadridSpain
  3. 3., Departamento de Análisis MatemáticoUniversidad de SevillaSevillaSpain

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
  • Copyright Information Springer Basel 2011
  • Publisher Name Springer, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0071-6
  • Softcover ISBN 978-3-0348-0328-1
  • eBook ISBN 978-3-0348-0072-3
  • Edition Number 1
  • Number of Pages XIV, 282
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Analysis
  • Buy this book on publisher's site
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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)