Geodesic
Interpolation theorems for the spaces $L_{p,q}$
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 229-242

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A sharp or optimal interpolation theorem is proved for the Lorentz spaces $L_{p,q}$, generalizing the Marcinkiewicz theorem and refining the Riesz–Thorin theorem and the Stein–Weiss theorem. This theorem extends to the spaces $\overline X_{\theta,p}$ of the real method constructed from any Banach pair; thus it extends also to Besov spaces. Bibliography: 12 titles. 
@article{SM_1989_64_1_a13,
     author = {V. I. Ovchinnikov},
     title = {Interpolation theorems for the spaces $L_{p,q}$},
     journal = {Sbornik. Mathematics},
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     volume = {64},
     number = {1},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/}
}
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V. I. Ovchinnikov. Interpolation theorems for the spaces $L_{p,q}$. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 229-242. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/