Variable Lebesgue Spaces Foundations and Harmonic Analysis /

• Main Authors: Cruz-Uribe, David V. (Author), Fiorenza, Alberto (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Basel : Springer Basel : Imprint: Birkhäuser, 2013.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Harmonic analysis.; Functional analysis.; Global analysis (Mathematics).; Manifolds (Mathematics).; Abstract Harmonic Analysis.; Functional Analysis.; Global Analysis and Analysis on Manifolds.

This book provides an accessible introduction to the theory of variable Lebesgue spaces. These spaces generalize the classical Lebesgue spaces by replacing the constant exponent p with a variable exponent p(x). They were introduced in the early 1930s but have become the focus of renewed interest sin...

Table of Contents:

•  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.        .