Weights, extrapolation and the theory of rubio defrancia

The extrapolation theorem of Rubio de Francia is one of the deepest results in the study of weighted norm inequalities in harmonic analysis. 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, we show how the key ideas can be used to extend the theory to a number of contexts.Our treatment generalizes and unifies all existing results in one-weight extrapolation theory. In the two-weight case we systematically develop a new approach to extrapolation and factorization that is closely tied to existing theoryof two-weight norm inequalities. We give a large number of applications that include both new results and new techniques that can be applied in other settings. 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. INDICE: 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. Chapter7. 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.

• ISBN: 978-3-0348-0071-6
• Editorial: Springer Basel
• Encuadernacion: Cartoné
• Páginas: 290
• Fecha Publicación: 31/03/2011
• Nº Volúmenes: 1
• Idioma: Inglés