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

Abstract

Let $\nu$ be a $\sigma$-finite Banach-space-valued measure defined on a $\delta$-ring. We find a wide class of measures $\nu$ for which interpolation with a parameter function of couples of Banach lattices of $p$-integrable and weakly $p$-integrable functions with respect to $\nu$ 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.