Geodesic
Characterization of optimal decompositions in real interpolation. II
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 179-185 Cet article a éte moissonné depuis la source Math-Net.Ru

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Optimal decompositions mentioned in the title have certain extremal properties expressed in terms of duality. We present a direct and fairly short proof of this. 
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S. V. Kislyakov; N. Ya. Kruglyak; J. Niyobuhungiro. Characterization of optimal decompositions in real interpolation. II. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part 42, Tome 424 (2014), pp. 179-185. http://geodesic.mathdoc.fr/item/ZNSL_2014_424_a5/

[1] N. Kruglyak, J. Niyobuhungiro, “Characterization of optimal decompositions in real Interpolation”, J. Approx. Theory, 185 (2014), 1–11 | DOI | MR | Zbl

[2] H. Attouch, H. Brezis, “Duality for the Sum of Convex Functions in General Banach Spaces”, Aspects of Mathematics and its Applications, ed. J. A. Barroso, North-Holland, Amsterdam, 1986, 125–133 | DOI | MR