Lorentz Spaces

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


The spaces considered in the previous chapters are one-parameter dependent. We now study the so-called Lorentz spaces which are a scale of function spaces which depend now on two parameters. Our first task therefore will be to define the Lorentz spaces and derive some of their properties, like completeness, separability, normability, duality among other topics, e.g., Hölder’s type inequality, Lorentz sequence spaces, and the spaces Lexp and LlogL, which were introduced by Zygmund and Titchmarsh.


Triangle Inequality Maximal Function Type Inequality Lebesgue Space Equivalent Norm 
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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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