General Reiteration Theorems for $${{\mathcal {R}}}$$ and $${{\mathcal {L}}}$$ Classes: Case of Right $${{\mathcal {R}}}$$-Spaces and Left $${{\mathcal {L}}}$$-Spaces

Abstract Given $$E_0, E_1, E, F$$ E 0 , 1 F rearrangement invariant spaces, $$a, \mathrm {b}, {b}_0, {b}_1$$ a b slowly varying functions and $$0\le \theta _0<\theta _1\le 1$$ ≤ θ < , we characterize the interpolation spaces $$\begin{aligned} ({\overline{X}}_{\theta _0,\mathrm {b}_0,E_0}, {\overline{X}}^{{\mathcal {R}}}_{\theta _1, {b}_1,E_1,a,F})_{\theta ,\mathrm {b},E}\quad \text {and}\quad ({\overline{X}}^{{\mathcal {L}}}_{\theta _0, {b}_0,E_0,a,F}, {\overline{X}}_{\theta _1,\mathrm {b}_1,E_1})_{\theta {b},E}, \end{aligned}$$ ( X ¯ R ) and L for all possible values of $$\theta \in [0,1]$$ ∈ [ ] . Applications to identities grand small Lebesgue Gamma A B -type are given.