Some Reiteration Theorems for R, L, RR, RL, LR, and LL Limiting Interpolation Spaces

Abstract

We consider the K-interpolation methods involving slowly varying functions. We establish some reiteration formulae including so-called L or R limiting interpolation spaces as well as the RR, RL, LR, and LL extremal interpolation spaces. These spaces arise in the limiting situations. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces in critical cases are given.