Extrapolation of vector-valued rearrangement operators

• Autores: Stefan Geiss, Paul F. X. Müller
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 3, 2009, págs. 798-814
• Idioma: inglés
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• Resumen

  • Given an injective map �Ñ :D �¨Dbetween the dyadic intervals of the unit interval [0, 1), we study extrapolation properties of the induced rearrangement operator of the Haar system IdX . Tp,�Ñ :

    Lp X,0([0, 1)) �¨ Lp X([0, 1)), where X is a Banach space and Lp X,0 the subspace of mean zero random variables. If X is a UMD-space, then we prove that the property that IdX . Tp,�Ñ is an isomorphism for some 1 < p = 2 < �� extrapolates across the entire scale of Lq X-spaces with 1 < q < ��. By contrast, if only IdX . Tp,�Ñ is bounded and not its inverse, then we prove one-sided extrapolation theorems and provide examples showing that this is best possible