Geodesic
Interpolation spaces between $(L_1^{w_0},L_1^{w_1})$ and $(L_1,L_\infty)$
Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 727-736.

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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. 
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     author = {V. I. Dmitriev},
     title = {Interpolation spaces between $(L_1^{w_0},L_1^{w_1})$ and $(L_1,L_\infty)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {727--736},
     publisher = {mathdoc},
     volume = {17},
     number = {5},
     year = {1975},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a5/}
}
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V. I. Dmitriev. Interpolation spaces between $(L_1^{w_0},L_1^{w_1})$ and $(L_1,L_\infty)$. Matematičeskie zametki, Tome 17 (1975) no. 5, pp. 727-736. http://geodesic.mathdoc.fr/item/MZM_1975_17_5_a5/