Holmstedt's formula for the K‐functional: the limit case θ0=θ1$\theta _0=\theta _1$

Abstract We consider K ‐interpolation spaces involving slowly varying functions, and derive necessary and sufficient conditions for a Holmstedt‐type formula to be held in the limiting case . We also study the case . Applications are given to Lorentz–Karamata spaces, generalized gamma spaces, and Besov spaces.