Geodesic
On a Peetre functional
Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 26-33 
G. M. Berkolaiko. On a Peetre functional. Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 26-33. http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a3/
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     author = {G. M. Berkolaiko},
     title = {On {a~Peetre} functional},
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     pages = {26--33},
     year = {1997},
     volume = {61},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a3/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

The Peetre $K$-functional is often used to describe and study the interpolation spaces associated with the real variable method. In the paper a modification of this functional, the Peetre $K_2$-functional $$ K_2(t,\mathbf x)=\inf_{\mathbf x=\mathbf x_1+\mathbf x_2}\sqrt{\|\mathbf x_1\|_1^2+t^2\|\mathbf x_2\|_2^2} $$ is treated as a function of $t$ for fixed $\mathbf x$, and its properties are studied. Several particular cases are considered and classes of functions expressible as $K_2(t)$ are investigated.

[1] Berg I., Lefstrem I., Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980

[2] Ovchinnikov V. I., “Interpolyatsionnye teoremy, vytekayuschie iz neravenstva Grotendika”, Funktsion. analiz i ego prilozh., 10:4 (1976), 45–54 | MR | Zbl

[3] Burbaki N., Funktsii deistvitelnogo peremennogo, Nauka, M., 1965