Geodesic
Extremal~$L_p$ interpolation in the mean with intersecting averaging intervals
Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 183-205.

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

We find the smallest constant $A=A(n,p,h)$ ($1$, $1$) such that for any sequence $y_k$, $k\in\mathbb Z$ whose $n$th differences are bounded by one in $l_p$ there is a function $f(x)$ with locally absolutely continuous $(n-1)$th derivative and with $n$th derivative in $L_p(\mathbb R)$ not exceeding $A$ that satisfies the mean interpolation conditions $\frac{1}{h}\,\int _{-h/2}^{h/2}f(k+t)\,dt=y_k$ ($k\in\mathbb Z$). Until now the solution to this problem was known only for non-intersecting averaging intervals ($0\geqslant h\geqslant 1$). 
@article{IM2_1997_61_1_a7,
     author = {Yu. N. Subbotin},
     title = {Extremal~$L_p$ interpolation in the mean with intersecting averaging intervals},
     journal = {Izvestiya. Mathematics },
     pages = {183--205},
     publisher = {mathdoc},
     volume = {61},
     number = {1},
     year = {1997},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a7/}
}
TY  - JOUR
AU  - Yu. N. Subbotin
TI  - Extremal~$L_p$ interpolation in the mean with intersecting averaging intervals
JO  - Izvestiya. Mathematics 
PY  - 1997
SP  - 183
EP  - 205
VL  - 61
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a7/
LA  - en
ID  - IM2_1997_61_1_a7
ER  - 
%0 Journal Article
%A Yu. N. Subbotin
%T Extremal~$L_p$ interpolation in the mean with intersecting averaging intervals
%J Izvestiya. Mathematics 
%D 1997
%P 183-205
%V 61
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a7/
%G en
%F IM2_1997_61_1_a7
Yu. N. Subbotin. Extremal~$L_p$ interpolation in the mean with intersecting averaging intervals. Izvestiya. Mathematics , Tome 61 (1997) no. 1, pp. 183-205. http://geodesic.mathdoc.fr/item/IM2_1997_61_1_a7/

[1] Subbotin Yu. N., “Funktsionalnaya interpolyatsiya v srednem s naimenshei $n$-i proizvodnoi”, Tr. MIAN SSSR, 88, Nauka, M., 1967, 30–60 | MR | Zbl

[2] Subbotin Yu. N., “Ekstremalnye zadachi funktsionalnoi interpolyatsii i interpolyatsionnye v srednem splainy”, Tr. MIAN SSSR, 138, Nauka, M., 1975, 118–173 | MR | Zbl

[3] Sharma A., Tsimbalario I., “Nekotorye lineinye differentsialnye operatory i obobschennye raznosti”, Matem. zametki, 21:2 (1977), 161–172 | MR | Zbl

[4] Shevaldin V. T., “Ob odnoi zadache funktsionalnoi interpolyatsii”, Matem. zametki, 29:4 (1981), 603–622 | MR | Zbl

[5] Shevaldin V. T., “Nekotorye zadachi ekstremalnoi interpolyatsii v srednem dlya lineinykh differentsialnykh operatorov”, Tr. MIAN SSSR, 164, Nauka, M., 1983, 203–240 | MR | Zbl

[6] Subbotin Yu. N., “Ekstremalnaya funktsionalnaya interpolyatsiya v srednem s naimenshim znacheniem $n$-i proizvodnoi pri bolshikh intervalakh usredneniya”, Matem. zametki, 59:1 (1996), 114–132 | MR