Resumen de Extreme cases of weak type interpolation

Evgeniy Pustylnik

• 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.