Here is an accessible introduction to the theory of variable Lebesgue spaces, beginning with the development of the basic function space properties, moving through harmonic analysis on variable Lebesgue spaces to basic results about variable Sobolev spaces.

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...

Divided into two parts, this book targets graduate students and researchers who want to learn about variable Lebesgue spaces and partial differential equations. Part I provides an introduction to the theory of variable Lebesgue spaces: Banach function spaces likethe classical Lebesgue spaces but with the constant exponent replaced by an exponent function. These spaces arise naturally in the study of partial differential equations and variational integrals with non-standard growth conditions. They have applications to electrorheological fluids in physics and to image reconstruction. Part IIof...