Geodesic
On the interpolation properties of certain quasilinearizable pairs
Sbornik. Mathematics, Tome 189 (1998) no. 2, pp. 227-234 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a quasilinearizable pair of reflexive spaces $\{A_0,A_1\}$, the interpolation properties of the derived pair $\{A_0+A_1,\ A_0\cap A_1\}$ are studied. A real interpolation formula is proved that connects the interpolation spaces of the pairs $\{A_0,A_1\}$ and $\{A_0+A_1,A_0\cap A_1\}$. In particular, it turns out that the corresponding interpolation spaces coincide for $\theta =\frac 12$. The results are applied to generalized Nikol'skii-Besov spaces (the quasilinearizability of a pair $\bigl \{B_{p,q}^1(\mu _0),B_{p,q}^1(\mu _1)\bigr \}$ of such spaces is proved beforehand). 
@article{SM_1998_189_2_a1,
     author = {A. G. Bagdasarian},
     title = {On the interpolation properties of certain quasilinearizable pairs},
     journal = {Sbornik. Mathematics},
     pages = {227--234},
     year = {1998},
     volume = {189},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/}
}
TY  - JOUR
AU  - A. G. Bagdasarian
TI  - On the interpolation properties of certain quasilinearizable pairs
JO  - Sbornik. Mathematics
PY  - 1998
SP  - 227
EP  - 234
VL  - 189
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/
LA  - en
ID  - SM_1998_189_2_a1
ER  - 
%0 Journal Article
%A A. G. Bagdasarian
%T On the interpolation properties of certain quasilinearizable pairs
%J Sbornik. Mathematics
%D 1998
%P 227-234
%V 189
%N 2
%U http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/
%G en
%F SM_1998_189_2_a1
A. G. Bagdasarian. On the interpolation properties of certain quasilinearizable pairs. Sbornik. Mathematics, Tome 189 (1998) no. 2, pp. 227-234. http://geodesic.mathdoc.fr/item/SM_1998_189_2_a1/

[1] Aronszajn N., Gagliardo E., “Interpolation spaces and interpolation methods”, Ann. Mat. Pura Appl. (4), 68 (1965), 51–117 | DOI | MR | Zbl

[2] Peetre J., “Zur Interpolation von Operatorenräume”, Arch. Math. (Basel), 21 (1970), 601–608 | MR

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

[4] Tribel Kh., Teoriya interpolyatsii. Funktsionalnye prostranstva. Differentsialnye operatory, Mir, M., 1980 | MR

[5] Peetre J., “Über den Durchschnitt von Interpolationsräumen”, Arch. Math. (Basel), 25 (1974), 511–513 | MR | Zbl

[6] Berens H., Interpolationsmethoden zur Behandlung von Approximationsprozessen auf Banachräumen, Lect. Notes in Math., 64, 1968 | MR | Zbl

[7] Triebel H., “General function spaces. III: Spaces $B_{p,q}^{g(x)}$ and $F_{p,q}^{g(x)}$, $1

\infty$: basic properties”, Anal. Math., 3 (1977), 221–249 | DOI | MR | Zbl

[8] Bagdasaryan A. G., “Ob interpolyatsii i sledakh funktsii iz nekotorykh anizotropnykh funktsionalnykh prostranstv”, Izv. AN Arm. SSR, 23:4 (1988), 353–365 | MR

[9] Lizorkin P. I., “$(L_p,L_q)$-multiplikatory integralov Fure”, Dokl. AN SSSR, 152 (1963), 808–811 | MR | Zbl

[10] Bagdasaryan A. G., “Interpolyatsiya nekotorykh funktsionalnykh prostranstv raznoi anizotropii”, Izv. AN Arm., 27:4 (1992), 49–52 | MR

[11] Bagdasaryan A. G., “Teoremy vlozheniya dlya nekotorykh obobschennykh funktsionalnykh prostranstv”, Izv. AN Arm., 29:3 (1994), 1–10 | MR | Zbl

[12] Volevich L. R., Paneyakh B. P., “Nekotorye prostranstva obobschennykh funktsii i teoremy vlozheniya”, UMN, 20:1 (1965), 3–74 | MR | Zbl