Geodesic
Lack of interpolation of linear operators in spaces of smooth functions
Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1229-1266

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

We prove that $C^k(\Omega)$, the space of $k$ times continuously differentiable functions on the closure of a region in a finite-dimensional manifold, is not an interpolation space between $C(\Omega)$ and $C^n(\Omega)$ for $0$. We find analogous results for the Sobolev–Stein spaces. In the class of spaces $C_\varphi$, defined by the modulus of continuity, we describe all interpolation spaces between $C$ and $C^2$. Bibliography: 34 titles. 
@article{IM2_1977_11_6_a4,
     author = {B. S. Mityagin and E. M. Semenov},
     title = {Lack of interpolation of linear operators in spaces of smooth functions},
     journal = {Izvestiya. Mathematics },
     pages = {1229--1266},
     publisher = {mathdoc},
     volume = {11},
     number = {6},
     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a4/}
}
TY  - JOUR
AU  - B. S. Mityagin
AU  - E. M. Semenov
TI  - Lack of interpolation of linear operators in spaces of smooth functions
JO  - Izvestiya. Mathematics 
PY  - 1977
SP  - 1229
EP  - 1266
VL  - 11
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a4/
LA  - en
ID  - IM2_1977_11_6_a4
ER  - 
%0 Journal Article
%A B. S. Mityagin
%A E. M. Semenov
%T Lack of interpolation of linear operators in spaces of smooth functions
%J Izvestiya. Mathematics 
%D 1977
%P 1229-1266
%V 11
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a4/
%G en
%F IM2_1977_11_6_a4
B. S. Mityagin; E. M. Semenov. Lack of interpolation of linear operators in spaces of smooth functions. Izvestiya. Mathematics , Tome 11 (1977) no. 6, pp. 1229-1266. http://geodesic.mathdoc.fr/item/IM2_1977_11_6_a4/