Collectanea mathematica

, Volume 62, Issue 1, pp 95–118 | Cite as

Capacitary function spaces

  • Joan Cerdà
  • Joaquim Martín
  • Pilar Silvestre


These notes are devoted to the analysis on a capacity space, with capacities as substitutes of measures in the study of function spaces. The goal is to extend to the associated function lattices some aspects of the theory of Banach function spaces, to show how the general theory can be applied to classical function spaces such as Lorentz spaces, and to complete the real interpolation theory for these spaces included in Cerdà (J Math Anal Appl 304:269–295, 2005) and Cerdà et al. (AMS Contemp Math 445:49–55, 2007).

Mathematics Subject Classification (2000)

Primary 46E30 Secondary 46B70 46M35 28A12 


Capacity Lorentz spaces Interpolation 


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© Universitat de Barcelona 2010

Authors and Affiliations

  1. 1.Departament de Matemàtica Aplicada i AnàlisiUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departament de MatemàtiquesUniversitat Autònoma de BarcelonaBellaterraSpain

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