Variable Lebesgue Spaces

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.

Proofs are developed in detail, illustrating the standard techniques used in the field? Accessible for research mathematicians as well as graduate students Provides a thorough and up to date bibliographic treatment that makes clear the history and development of the field Includes supplementary material: sn.pub/extras

Inhalt
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.