Interpolation with a parameter function of Lp-spaces with respect to a vector measure on a δ-ring

Abstract

Let ν be a σ-finite Banach-space-valued measure defined on a δ-ring. We find a wide class of measures ν for which interpolation with a parameter function of couples of Banach lattices of p-integrable and weakly p-integrable functions with respect to ν produces a Lorentz-type space. Moreover, we prove that if we interpolate between sums and intersections of them, then they still yield another Lorentz-type space closely related with the first one