Extreme cases of weak type interpolation

  • Evgeniy Pustylnik

    Technion - Israel Institute of Technology, Haifa, Israel


We consider quasilinear operators of joint weak type (in the sense of [Bennett, Sharpley: Interpolation of operators, Academic Press, 1988]) and study their properties on spaces with the norm , where is arbitrary rearrangement-invariant space with respect to the measure . A space is said to be “close" to one of the endpoints of interpolation if the corresponding Boyd index of this space is equal to or to . For all possible kinds of such “closeness”, we give sharp estimates for the function so as to obtain that every .

Cite this article

Evgeniy Pustylnik, Extreme cases of weak type interpolation. Rev. Mat. Iberoam. 21 (2005), no. 2, pp. 557–576

DOI 10.4171/RMI/429