, Volume 22, Issue 1, pp 63–81 | Cite as

Local rearrangement invariant spaces and distribution of Rademacher series

  • Javier Carrillo-Alanís


We prove that a local version of Khintchine inequality holds for arbitrary rearrangement invariant (r.i.) spaces on an non-empty open set \(E\subset [0,1]\). For this, we give a definition of local r.i. space which is compatible with the notion of systems equivalent in distribution and prove that the Rademacher system \((r_{k+N})_{k=1}^\infty \) on an non-empty open set E is equivalent in distribution to \((r_k)_{k=1}^\infty \) on [0, 1], with N depending on E. The result can be generalized to a wider class of sets.


Function spaces Rademacher series Rearrangement invariant spaces Distribution function 

Mathematics Subject Classification

46E30 60E99 



This work is part of the Ph.D. thesis of the author which is being prepared at University of Sevilla under the supervision of Prof. G. P. Curbera.


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Copyright information

© Springer International Publishing 2017

Authors and Affiliations

  1. 1.Universidad de Sevilla SevilleSevilleSpain

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