Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

A note on function spaces generated by Rademacher series

Guillermo P. Curberaa1*

a1 Facultad De Matemáticas, Universidad de Sevilla, Aptdo (P.O. Box) 1160, Sevilla 41080, Spain E-mail address: curbera@cica.es

Abstract

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 fgxs2208X for every function g=∑bnrn where (bn)xs22082. 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.

(Received March 29 1995)

Footnotes

* Research supported in part by DGICYT grant #PB93–0926.