Interpolation spaces between $(L_1^{w_0},L_1^{w_1})$ and $(L_1,L_\infty)$

Let $A_0,A_1$ be a pair of normed spaces, having the property that the difference $K(x,t;A_0,A_1)-K(x,s;A_0,A_1)$ regarded as a function of $x\in A_0+A_1$ is a seminorm for $t>s$ (here $K$ is the Oklander–Peetre functional). All the pairs $A,L$ of normed spaces, such that, if a linear operator is bounded from $A_0$ into $L_1$ and from $A_1$ into $L_\infty$, then it is bounded from $A$ into $L$, are characterized in the following article.