JOINT WEAK TYPE INTERPOLATION ON LORENTZ-KARAMATA SPACES

We present sharp interpolation theorems, including all limiting cases, for a class of quasilinear operators of joint weak type acting between Lorentz-Karamata spaces over sigma-finite measure. This class contains many of the important integral operators. The optimality in the scale of Lorentz-Karamata spaces is also discussed. The proofs of our results rely on a characterization of Hardy-type inequalities restricted to monotone functions and with power-slowly varying weights. Some of the limiting cases of these inequalities have not been considered in the literature so far.