We consider K-interpolation methods involving slowly varying functions. Let $\overline{ A}_{ \theta,*}^{ \mathcal{ L}}$ and $\overline{ A}_{ \theta,*}^{ \mathcal{ R}}$ $(0\leq\theta\leq1)$ be the so called ${ \mathcal{ L}}$ or ${ \mathcal{ R}}$ limiting interpolation spaces which arise naturally in reiteration formulae for the limiting cases. We characterize the interpolation spaces $\Big(\overline{ A}_{ \theta_0,*}^{ \mathcal{ L}}, *\Big)_{ \eta,r,a}$, $\Big(\overline{ A}_{ \theta_0,*}^{ \mathcal{ R}}, *\Big)_{ \eta,r,a}$, $\Big(*, \overline{ A}_{ \theta_1,*}^{ \mathcal{ L}}\Big)_{ \eta,r,a}$, and $\Big(*, \overline{ A}_{ \theta_1,*}^{ \mathcal{ R}}\Big)_{ \eta,r,a}$ $(0\leq\eta\leq1)$ for the limiting cases $\theta_0=0$ and $\theta_1=1$. This supplements the earlier papers of the authors, which only considered the case $0<\theta_0<\theta_1<1$. The proofs of most reiteration formulae are based on Holmstedt-type formulae. Applications to grand and small Lorentz spaces as well as to Lorentz-Karamata spaces are given.
Categories: math.FA