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Variable Exponent Lebesgue Spaces

  • Lars DieningEmail author
  • Petteri Harjulehto
  • Peter Hästö
  • Michael Růžička
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2017)

Abstract

In this chapter we define Lebesgue spaces with variable exponents, \(L^{p(.)}\). They differ from classical \(L^p\) spaces in that the exponent p is not constant but a function from Ω to \([1,\infty]\). The spaces \(L^{p(.)}\) fit into the framework of Musielak–Orlicz spaces and are therefore also semimodular spaces.

Keywords

Simple Function Lebesgue Space Orlicz Space Variable Exponent Banach Function Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Lars Diening
    • 1
    Email author
  • Petteri Harjulehto
    • 2
  • Peter Hästö
    • 3
  • Michael Růžička
    • 4
  1. 1.Institute of MathematicsLMU MunichMunichGermany
  2. 2.Department of Mathematics and StatisticsUniversity of HelsinkiHelsinkiFinland
  3. 3.Department of Mathematical SciencesUniversity of OuluOuluFinland
  4. 4.Institute of MathematicsUniversity of FreiburgFreiburgGermany

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