منابع مشابه
Extrapolation of vector-valued rearrangement operators II
We determine the extrapolation law of rearrangement operators acting on the Haar system in vector valued H spaces: If 0 < q ≤ p < 2, then, ‖Tτ,q ⊗ IdX‖ q 2−q q ≤ A(p, q)‖Tτ,p ⊗ IdX‖ p 2−p p . For a fixed Banach space X, the extrapolation range 0 < q ≤ p < 2 is optimal. If, however, there exists 1 < p0 < ∞, so that ‖Tτ,p0 ⊗ IdE‖L0 E < ∞, for each UMD space E, then for any 1 < p < ∞, ‖Tτ,p ⊗ IdE‖...
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Given an injective map τ : D → D between the dyadic intervals of the unit interval [0, 1), we study extrapolation properties of the induced rearrangement operator of the Haar system IdX ⊗ Tp,τ : L p X,0([0, 1)) → L p X([0, 1)), where X is a Banach space and L p X,0 the subspace of mean zero random variables. If X is a UMD-space, then we prove that the property that IdX ⊗ Tp,τ is an isomorphism ...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 2015
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/hav031