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Local Khintchine inequality in rearrangement invariant spaces

  • Serguey V. Astashkin
  • Guillermo P. CurberaEmail author
Article

Abstract

We prove that the local version of Khintchine inequality holds in an rearrangement invariant function space \(X\) on [0,1] if and only if the lower dilation index of the fundamental function of \(X\) is positive. A further characterization is given, based on the uniform behavior in \(X\) of the dilations of the logarithmic function. For this, a study of the space of functions acting as multiplication operators in \(X\) for the tails of Rademacher series is carried out.

Keywords

Rademacher functions Rearrangement invariant space  Khintchine inequality 

Mathematics Subject Classification (2000)

Primary 46E35 46E30 Secondary 47G10 

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Copyright information

© Fondazione Annali di Matematica Pura ed Applicata and Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Department of Mathematics and MechanicsSamara State UniversitySamaraRussia
  2. 2.Facultad de MatemáticasUniversidad de SevillaSevillaSpain

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