Weak Lebesgue Spaces

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


In this chapter we study the so-called weak Lebesgue spaces which are one of the first generalizations of the Lebesgue spaces and a prototype of the so-called Lorentz spaces which will be studied in a subsequent chapter. In the framework of weak Lebesgue spaces we will study, among other topics, embedding results, convergence in measure, interpolation results, and the question of normability of the space. We also show a Fatou type lemma for weak Lebesgue spaces as well as the completeness of the quasi-norm. The Lyapunov inequality and the Hölder inequality are shown to hold.


  1. [5]
    R. E. Castillo, F. Vallejo Narvaez, and J.C. Ramos Fernández. Multiplication and composition operators on weak l p spaces. Bull. Malays. Math. Sci. Soc., 38(3):927–973, 2015.MathSciNetCrossRefzbMATHGoogle Scholar

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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