Geodesic
Interpolation theorems for the spaces $L_{p,q}$
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 229-242 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A sharp or optimal interpolation theorem is proved for the Lorentz spaces $L_{p,q}$, generalizing the Marcinkiewicz theorem and refining the Riesz–Thorin theorem and the Stein–Weiss theorem. This theorem extends to the spaces $\overline X_{\theta,p}$ of the real method constructed from any Banach pair; thus it extends also to Besov spaces. Bibliography: 12 titles. 
@article{SM_1989_64_1_a13,
     author = {V. I. Ovchinnikov},
     title = {Interpolation theorems for the spaces $L_{p,q}$},
     journal = {Sbornik. Mathematics},
     pages = {229--242},
     year = {1989},
     volume = {64},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/}
}
TY  - JOUR
AU  - V. I. Ovchinnikov
TI  - Interpolation theorems for the spaces $L_{p,q}$
JO  - Sbornik. Mathematics
PY  - 1989
SP  - 229
EP  - 242
VL  - 64
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/
LA  - en
ID  - SM_1989_64_1_a13
ER  - 
%0 Journal Article
%A V. I. Ovchinnikov
%T Interpolation theorems for the spaces $L_{p,q}$
%J Sbornik. Mathematics
%D 1989
%P 229-242
%V 64
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/
%G en
%F SM_1989_64_1_a13
V. I. Ovchinnikov. Interpolation theorems for the spaces $L_{p,q}$. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 229-242. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a13/

[1] Ovchinnikov V. I., “Tochnaya interpolyatsionnaya teorema v prostranstvakh $L_p$”, DAN SSSR, 272:2 (1983), 300–303 | MR | Zbl

[2] Bennett G., “Inclusion mappings between $l^p$-spaces”, J. Funct. Analyt., 13 (1973), 20–27 | DOI | MR | Zbl

[3] Berg I., Lefstrem Ya., Interpolyatsionnye prostranstva. (Vvedenie), Mir, M., 1980 | MR

[4] Holmstedt J., “Interpolation of quasi-normed spaces”, Math. Scand., 26 (1970), 177–199 | MR | Zbl

[5] Aronszajn N., Galgiardo E., “Interpolation spaces and interpolation methods”, Ann. Mat. Pura Appl., 68 (1965), 51–118 | DOI | MR

[6] Janson S., “On the interpolation of sublinear operators”, Studia Math., 75:1 (1982), 51–53 | MR | Zbl

[7] Ovchinnikov V. I., “The method of orbits in interpolation theory”, Math. Reports., 1 (1984), 349–516 | MR

[8] Ovchinnikov V. I., “Ob otsenkakh interpolyatsionnykh orbit”, Matem. sb., 115(157) (1981), 642–652 | MR | Zbl

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

[10] Calderon A. P., “Spaces between $L^1$ and $L^{\infty}$ and the theorem of Marcinkiewicz”, Studia Math., 26 (1966), 273–299 | MR | Zbl

[11] Kashin B. S, Saakyan A. A., Ortogonalnye ryady, Nauka, M., 1984 | MR | Zbl

[12] Semyonov E. M., “On the boundedness of operators rearranging the Haar system in the spaces $L_p$”, Integral Equations and Operator Theory, 6 (1983), 385–404 | DOI | MR | Zbl