Journal d'Analyse Mathématique

, Volume 134, Issue 1, pp 237–254 | Cite as

A counting problem in ergodic theory and extrapolation for one-sided weights

  • María J. Carro
  • María Lorente
  • Francisco J. Martín-Reyes


The purpose of this paper is to prove that, given a dynamical system (X,M,μ, τ) and 0 < q < 1, the Lorentz spaces L1,q(μ) satisfy the so-called Return Times Property for the Tail, contrary to what happens in the case q = 1. In fact, we consider a more general case than in previous papers since we work with a σ-finite measure μ and a transformation τ which is only Cesàro bounded. The proof uses the extrapolation theory of Rubio de Francia for one-sided weights. These results are of independent interest and can be applied to many other situations.


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Copyright information

© Hebrew University Magnes Press 2018

Authors and Affiliations

  • María J. Carro
    • 1
  • María Lorente
    • 2
  • Francisco J. Martín-Reyes
    • 2
  1. 1.Departament de Matemàtica Aplicada I AnàlisiUniversitat de BarcelonaBarcelonaSpain
  2. 2.Departamento de Anàlisis Matemático, Facultad de CienciasUniversidad de MálagaMálagaSpain

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