Variable Exponent Lebesgue Spaces

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


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.


Simple Function Lebesgue Space Orlicz Space Variable Exponent Banach Function Space 
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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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