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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...

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of the...

This monograph provides a state-of-the-art, self-contained account on the effectiveness of the method of boundary layer potentials in the study of elliptic boundary value problems with boundary data in a multitude of function spaces. Many significant new results are explored in detail, with complete proofs, emphasizing and elaborating on the link between the geometric measure-theoretic features of an underlying surface and the functional analytic properties of singular integral operators defined on it. Graduate students, researchers, and professionals interested in a modern account of...

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...