Geodesic
On a Peetre functional
Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 26-33 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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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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