Reiteration theorem for [formula omitted] and [formula omitted]-spaces with the same parameter

Abstract

Let E,F,E0,E1 be rearrangement invariant spaces; let a,b,b0,b1 be slowly varying functions and 0<θ0,θ1<1. We characterize the interpolation spaces(X‾θ0,b0,E0,a,FR,X‾θ1,b1,E1,a,FL)η,b,E,0≤η≤1, when the parameters θ0 and θ1 are equal (under appropriate conditions on bi(t), i=0,1). This completes the study started in [11,12,22], which only considered the case θ0<θ1. As an application we recover and generalize interpolation identities for grand and small Lebesgue spaces given by [26].