A note on function spaces generated by Rademacher series
GP Curbera - Proceedings of the Edinburgh Mathematical Society, 1997 - cambridge.org
Proceedings of the Edinburgh Mathematical Society, 1997•cambridge.org
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 …
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 …
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.
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