Extreme cases of weak type interpolation

• Autores: Evgeniy Pustylnik
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 21, Nº 2, 2005, págs. 557-576
• Idioma: inglés
• DOI: 10.4171/rmi/429
• Títulos paralelos:
  • Casos extremos de interpolación de tipo débil.
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• Resumen

  • We consider quasilinear operators T of joint weak type (a, b; p, q) (in the sense of [2]) and study their properties on spaces L?,E with the norm ||?(t) f*(t)||Ê, where Ê is arbitrary rearrangement-invariant space with respect to the measure dt/t. A space L?,E is said to be "close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to 1/a or to 1/p. For all possible kinds of such "closeness", we give sharp estimates for the function ?(t) so as to obtain that every T: L?,E ? L?,E.