Geodesic
The inverse interpolation problem for operators
Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 323-333.

Voir la notice de l'article provenant de la source Math-Net.Ru

The inverse problem for a real interpolation functor in the class of ideal spaces is discussed. The most complete solution is obtained for consistent interpolation couples. It follows from the theorems proved in this article and from the concepts introduced that the Marcinkiewicz theorem on interpolation of weak type operators cannot essentially be strengthened. 
@article{MZM_1996_59_3_a0,
     author = {E. I. Berezhnoi},
     title = {The inverse interpolation problem for operators},
     journal = {Matemati\v{c}eskie zametki},
     pages = {323--333},
     publisher = {mathdoc},
     volume = {59},
     number = {3},
     year = {1996},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a0/}
}
TY  - JOUR
AU  - E. I. Berezhnoi
TI  - The inverse interpolation problem for operators
JO  - Matematičeskie zametki
PY  - 1996
SP  - 323
EP  - 333
VL  - 59
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a0/
LA  - ru
ID  - MZM_1996_59_3_a0
ER  - 
%0 Journal Article
%A E. I. Berezhnoi
%T The inverse interpolation problem for operators
%J Matematičeskie zametki
%D 1996
%P 323-333
%V 59
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a0/
%G ru
%F MZM_1996_59_3_a0
E. I. Berezhnoi. The inverse interpolation problem for operators. Matematičeskie zametki, Tome 59 (1996) no. 3, pp. 323-333. http://geodesic.mathdoc.fr/item/MZM_1996_59_3_a0/

[1] Korotkov V. B., Integralnye operatory, Nauka, Novosibirsk, 1983

[2] Jones P., “Factorization of $A_p$-weights”, Ann. Math., 111:3 (1980), 511–530 | DOI | MR | Zbl

[3] Muckenhoupt B., “Weighted norm inegualities for the Hardy maximal function”, Trans. Amer. Math. Soc., 165 (1972), 207–226 | DOI | MR | Zbl

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

[5] Brudniy Yu., Kruglyak N., Interpolation functions and interpolation spaces, North Holland Press, Amsterdam, 1991

[6] Krein S. G., Petunin Yu. I., Semenov E. M., Interpolyatsiya lineinykh operatorov, Nauka, M., 1978

[7] Kantorovich L. V., Akilov G. P., Funktsionalnyi analiz, Nauka, M., 1977 | Zbl

[8] Lindenstrauss J., Tzafriri L., Classical Banach Spaces, V. I, Springer, Berlin, 1973; V. II, 1979

[9] Mazya V. G., Prostranstva S. L. Soboleva, Izd-vo LGU, L., 1985 | Zbl

[10] Berezhnoi E. I., Zabreiko P. P., “Interpolyatsiya chastichno additivnykh operatorov”, Dokl. AN BSSR, XXX:2 (1986), 108–111 | MR

[11] Berezhnoi E. I., Zabreico P. P., “Some intherpolation theory for nonlinear operators”, Nonlinear Analysis, 12:2 (1988), 155–170 | DOI | MR