Geodesic
Interpolation properties of scales of Banach spaces
Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 803-813 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

It is shown that any interpolation scales joining weight spaces $L_p$ or similar spaces have many remarkable properties. Not only are such scales intrinsically interpolation scales, but an analog of the Arazy–Cwikel theorem describing interpolation spaces between the spaces from the scale is valid. 
@article{MZM_2006_80_6_a0,
     author = {Yu. N. Bykov and V. I. Ovchinnikov},
     title = {Interpolation properties of scales of {Banach} spaces},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--813},
     year = {2006},
     volume = {80},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a0/}
}
TY  - JOUR
AU  - Yu. N. Bykov
AU  - V. I. Ovchinnikov
TI  - Interpolation properties of scales of Banach spaces
JO  - Matematičeskie zametki
PY  - 2006
SP  - 803
EP  - 813
VL  - 80
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a0/
LA  - ru
ID  - MZM_2006_80_6_a0
ER  - 
%0 Journal Article
%A Yu. N. Bykov
%A V. I. Ovchinnikov
%T Interpolation properties of scales of Banach spaces
%J Matematičeskie zametki
%D 2006
%P 803-813
%V 80
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a0/
%G ru
%F MZM_2006_80_6_a0
Yu. N. Bykov; V. I. Ovchinnikov. Interpolation properties of scales of Banach spaces. Matematičeskie zametki, Tome 80 (2006) no. 6, pp. 803-813. http://geodesic.mathdoc.fr/item/MZM_2006_80_6_a0/

[1] I. Berg, I. Lëfstrëm, Interpolyatsionnye prostranstva. Vvedenie, Mir, M., 1980 | MR | Zbl

[2] S. G. Krein, Yu. I. Petunin, E. M. Semenov, Interpolyatsiya lineinykh operatorov, Nauka, M., 1978 | MR | Zbl

[3] Y. Arazy, M. Cwikel, “A new characterization of the interpolation spaces between $L_p$ and $L_q$”, Math. Scand., 55:2 (1984), 253–270 | MR | Zbl

[4] G. Sparr, “Interpolation of weighted $L_p$ spaces”, Studia Math., 62 (1978), 229–271 | MR | Zbl

[5] V. I. Ovchinnikov, “The method of orbits in interpolation theory”, Math. Rep. Ser. 1, 1:2 (1984), 349–515 | MR | Zbl