Weights, Extrapolation and the Theory of Rubio De Francia

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 theory of 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.