Duals of limiting interpolation spaces

The aim of the paper is to establish duals of the limiting real interpolation $K$- and $J$-spaces $(X_0,X_1{)}_{0,q,v;K}$ and $(X_0,X_1{)}_{0,q,v;J}$, where $(X_0,X_1)$ is a compatible couple of Banach spaces, $1\le q<\mathrm{\infty }$, $v$ is a slowly varying function on the interval $(0,\mathrm{\infty })$, and the symbols $K$ and $J$ stand for the Peetre $K$- and $J$-functionals. In the case of the classical real interpolation method $(X_0,X_1{)}_{\theta ,q}$, where $\theta \in (0,1)$ and $1\le q<\mathrm{\infty }$, this problem was solved by Lions and Peetre.