Nonstandard Lebesgue Spaces

  • René Erlín Castillo
  • Humberto Rafeiro
Part of the CMS Books in Mathematics book series (CMSBM)


In recent years, it had become apparent that the plethora of existing function spaces were not sufficient to model a wide variety of applications, e.g., in the modeling of electrorheological fluids, thermorheological fluids, in the study of image processing, in differential equations with nonstandard growth, among others. Thus, naturally, new fine scales of function spaces have been introduced, namely variable exponent spaces and grand spaces. In this chapter we study variable exponent Lebesgue spaces and grand Lebesgue spaces. In variable exponent Lebesgue spaces we study the problem of normability, denseness, completeness, embedding, among others. We give a brisk introduction to grand Lebesgue spaces via Banach function space theory, dealing with the problem of normability, embeddings, denseness, reflexivity, and the validity of a Hardy inequality in the aforementioned spaces.


Lebesgue Space Hardy Inequality Translation Operator Banach Function Space Conjugate Exponent 
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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • René Erlín Castillo
    • 1
  • Humberto Rafeiro
    • 2
  1. 1.Universidad Nacional de ColombiaBogotáColombia
  2. 2.Pontificia Universidad JaverianaBogotáColombia

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