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    Curbera, Guillermo P. and Ricker, Werner J. 2016. Abstract Cesàro spaces: Integral representations. Journal of Mathematical Analysis and Applications, Vol. 441, Issue. 1, p. 25.

    Astashkin, Serguey V. and Curbera, Guillermo P. 2015. Local Khintchine inequality in rearrangement invariant spaces. Annali di Matematica Pura ed Applicata (1923 -), Vol. 194, Issue. 3, p. 619.

    Astashkin, S. V. 2010. Rademacher functions in symmetric spaces. Journal of Mathematical Sciences, Vol. 169, Issue. 6, p. 725.

    Astashkin, Serguei V. and Curbera, Guillermo P. 2009. Rearrangement invariance of Rademacher multiplicator spaces. Journal of Functional Analysis, Vol. 256, Issue. 12, p. 4071.

    Astashkin, Serguei V. and Curbera, Guillermo P. 2005. Symmetric kernel of Rademacher multiplicator spaces. Journal of Functional Analysis, Vol. 226, Issue. 1, p. 173.

    Асташкин, Сергей Владимирович and Astashkin, Sergei Vladimirovich 2004. О пространстве мультипликаторов, порожденном системой Радемахера. Математические заметки, Vol. 75, Issue. 2, p. 173.

    Курбера, Г П Curbera, Guillermo P Родин, Владимир Александрович and Rodin, Vladimir Aleksandrovich 2002. О мультипликаторах на множестве рядов Радемахера в симметричных пространствах. Функциональный анализ и его приложения, Vol. 36, Issue. 3, p. 87.

  • Proceedings of the Edinburgh Mathematical Society, Volume 40, Issue 1
  • February 1997, pp. 119-126

A note on function spaces generated by Rademacher series

  • Guillermo P. Curbera (a1)
  • DOI:
  • Published online: 01 February 1997

Let X be a rearrangement invariant function space on [0,1] in which the Rademacher functions (rn) generate a subspace isomorphic to ℓ2. We consider the space Λ(R, X) of measurable functions f such that fgX for every function g=∑bnrn where (bn)∈ℓ2. We show that if X satisfies certain conditions on the fundamental function and on certain interpolation indices then the space Λ(R, X) is not order isomorphic to a rearrangement invariant space. The result includes the spaces Lp, q and certain classes of Orlicz and Lorentz spaces. We also study the cases X = Lexp and X = Lψ2 for ψ2) = exp(t2) – 1.

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1.C. Bennett and R. Sharpley , Interpolation of operators (Academic Press, Inc., Boston, 1988).

2.D. W. Boyd , The Hilbert transform on rearrangement-invariant spaces, Canad. J. Math. 19 (1967), 599616.

3.G. P. Curbera , Banach space properties of L1 of a vector measure, Proc. Amer. Math. Soc. 123 (1995), 37973806.

5.J. Lindenstrauss and L. Tzafriri , Classical Banach Spaces, vol. II (Springer-Verlag, Berlin, New York, 1979).

6.V. A. Rodin and E. M. Semenov , Rademacher series in symmetric spaces, Anal. Math. 1 (1975), 207222.

7.R. Sharpley , Spaces Λx(X) and interpolation, J. Funct. Anal. 11 (1972), 479513.

8.M. Zippin , Interpolation of operators of weak type between rearrangement-invariant function spaces, J. Funct. Anal. 7 (1971), 267284.

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Proceedings of the Edinburgh Mathematical Society
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