Weights, Extrapolation and the Theory of Rubio de Francia (Operator Theory: Advances and Applications Book 215)

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. Front Matter....Pages i-xiii Front Matter....Pages 1-1 Introduction to Norm Inequalities and Extrapolation....Pages 3-16 The Essential Theorem....Pages 17-26 Extrapolation for Muckenhoupt Bases....Pages 27-63 Extrapolation on Function Spaces....Pages 65-93 Front Matter....Pages 95-95 Preliminary Results....Pages 97-121 Two-Weight Factorization....Pages 123-134 Two-Weight Extrapolation....Pages 135-162 Endpoint and A ∞ Extrapolation....Pages 163-174 Applications of Two-Weight Extrapolation....Pages 175-200 Further Applications of Two-Weight Extrapolation....Pages 201-236 Back Matter....Pages 237-280