Collectanea mathematica

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

Capacitary function spaces

Article

Abstract

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 

Keywords

Capacity Lorentz spaces Interpolation 

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Copyright information

© 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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