Weights, Extrapolation and the Theory of Rubio de Francia

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.

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.

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

Inhalt

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.