Variable Lebesgue Spaces

From the reviews: "This book is eminently well suited to graduate students who have had standard courses in Lebesgue integration and functional analysis ... . this is a timely and exceedingly well-written book regarding variable Lebesgue spaces--one that provides the reader with fundamental analytic tools in the subject, an introduction to harmonic analysis on variable Lebesgue spaces, and a clear orientation on where to go to engage in profitable research in this rapidly developing area of analysis." (Paul Alton Hagelstein, Mathematical Reviews, September, 2013)

• 1 Introduction.- 2 Structure of Variable Lebesgue Spaces.- 3 The Hardy-Littlewood Maximal Operator.- 4 Beyond Log-Hölder Continuity.- 5 Extrapolation in the Variable Lebesgue Spaces.- 6 Basic Properties of Variable Sobolev Spaces.- Appendix: Open Problems.- Bibliography.- Symbol Index.- Author Index.- Subject Index.       ​