General Reiteration Theorems for R and L Classes: Case of Right R-Spaces and Left L-Spaces (2010.06940v1)

Abstract: Given $E_0, E_1, E, F$ rearrangement invariant spaces, $a, b, b_0, b_1$ slowly varying functions and $0\leq \theta_0<\theta_1\leq 1$, we characterize the interpolation space $$(\overline{X}{\theta_0,b_0,E_0}, \overline{X}^{\mathcal R}{\theta_1, b_1,E_1,a,F}){\theta,b,E} \quad \text{and} \quad (\overline{X}^{\mathcal L}{\theta_0, b_0,E_0,a,F}, \overline{X}{\theta_1,b_1,E_1}){\theta,b,E},$$ for all possible values of $\theta\in[0,1]$. Applications to interpolation identities for grand and small Lebesgue spaces, Gamma spaces and $A$ and $B$-type spaces are given.