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A note on function spaces generated by Rademacher series

Published online by Cambridge University Press:  20 January 2009

Guillermo P. Curbera
Guillermo P. Curbera
Affiliation:
Facultad De Matemáticas, Universidad de Sevilla, Aptdo (P.O. Box) 1160, Sevilla 41080, Spain E-mail address: [email protected]
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Abstract

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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 fg∈X 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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 40 , Issue 1 , February 1997 , pp. 119 - 126
Copyright
Copyright © Edinburgh Mathematical Society 1997

References

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