On the range space of Yano's extrapolation theorem and new extrapolation estimates at infinity

• Autores: María Jesús Carro Rossell
• Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 46, Nº Extra 1, 2002, págs. 27-37
• Idioma: inglés
• DOI: 10.5565/publmat_esco02_02
• Títulos paralelos:
  • Sobre el espacio de rango del teorema de extrapolación de Yano y nuevas estimaciones de extrapolación en el infinito
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• Resumen

  • Given a sublinear operator T satisfying that ||Tf||Lp(?) = C/(p-1) ||f||Lp(µ), for every 1 < p = p0, with C independent of f and p, it was proved in [C] that... [check the paper abstract for the formula] This estimate implies that T: L log L ? B, where B is a rearrangement invariant space. The purpose of this note is to give several characterizations of the space B and study its associate space. This last information allows us to formulate an extrapolation result of Zygmund type for linear operators satisfying ||Tf||Lp(?) = Cp|| f ||Lp(µ), for every p = p0.

    [Proceedings of the 6th International Conference on Harmonic Analysis and Partial Differential Equations, El Escorial (Madrid), 2002].