General Reiteration Theorems for R and L Classes: Case of Right R-Spaces and Left L-Spaces

Abstract

Given $E_0,E_1,E,F$ rearrangement invariant spaces, $a,b,b_0,b_1$ slowly varying functions and $0\le {\theta }_0<{\theta }_1\le 1$, we characterize the interpolation space $$({\overline{X}}_{{\theta }_0,b_0,E_0},{\overline{X}}_{{\theta }_1,b_1,E_1,a,F}^{\mathcal{R}}{)}_{\theta ,b,E}\text{and}({\overline{X}}_{{\theta }_0,b_0,E_0,a,F}^{\mathcal{L}},{\overline{X}}_{{\theta }_1,b_1,E_1}{)}_{\theta ,b,E},$$ 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.

References in corpus (1)

• Lorentz--Karamata spaces