Geodesic
On a~Peetre functional
Matematičeskie zametki, Tome 61 (1997) no. 1, pp. 26-33

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. 
@article{MZM_1997_61_1_a3,
     author = {G. M. Berkolaiko},
     title = {On {a~Peetre} functional},
     journal = {Matemati\v{c}eskie zametki},
     pages = {26--33},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a3/}
}
TY  - JOUR
AU  - G. M. Berkolaiko
TI  - On a~Peetre functional
JO  - Matematičeskie zametki
PY  - 1997
SP  - 26
EP  - 33
VL  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a3/
LA  - ru
ID  - MZM_1997_61_1_a3
ER  - 
%0 Journal Article
%A G. M. Berkolaiko
%T On a~Peetre functional
%J Matematičeskie zametki
%D 1997
%P 26-33
%V 61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1997_61_1_a3/
%G ru
%F MZM_1997_61_1_a3
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/