Synopses & Reviews
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.
Review
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)
Review
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)
Synopsis
This book provides a comprehensive treatment of extrapolation theory. Starting from an extremely clear and simple proof of the classical result of Rubio de Francia, the authors show how the key ideas can be used to extend the theory to a variety of contexts.
Table of Contents
Preface.- Preliminaries.- Part I. One-Weight Extrapolation.- Chapter 1. Introduction to Norm Inequalities and Extrapolation.- Chapter 2. The Essential Theorem.- Chapter 3. Extrapolation for Muckenhoupt Bases.- Chapter 4. Extrapolation on Function Spaces.- Part II. Two-Weight Factorization and Extrapolation.- Chapter 5. Preliminary Results.- Chapter 6. Two-Weight Factorization.- Chapter 7. Two-Weight Extrapolation.- Chapter 8. Endpoint and A1 Extrapolation.- Chapter 9. Applications of Two-Weight Extrapolation.- Chapter 10. Further Applications of Two-Weight Extrapolation.- Appendix A. The Calderón-Zygmund Decomposition.- Bibliography.- Index.