Geodesic
Approximation by rational functions in integral metrics and differentiability in the mean
Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 801-811 
E. P. Dolzhenko; E. A. Sevast'yanov. Approximation by rational functions in integral metrics and differentiability in the mean. Matematičeskie zametki, Tome 16 (1974) no. 5, pp. 801-811. http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a14/
@article{MZM_1974_16_5_a14,
     author = {E. P. Dolzhenko and E. A. Sevast'yanov},
     title = {Approximation by rational functions in integral metrics and differentiability in the mean},
     journal = {Matemati\v{c}eskie zametki},
     pages = {801--811},
     year = {1974},
     volume = {16},
     number = {5},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a14/}
}
TY  - JOUR
AU  - E. P. Dolzhenko
AU  - E. A. Sevast'yanov
TI  - Approximation by rational functions in integral metrics and differentiability in the mean
JO  - Matematičeskie zametki
PY  - 1974
SP  - 801
EP  - 811
VL  - 16
IS  - 5
UR  - http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a14/
LA  - ru
ID  - MZM_1974_16_5_a14
ER  - 
%0 Journal Article
%A E. P. Dolzhenko
%A E. A. Sevast'yanov
%T Approximation by rational functions in integral metrics and differentiability in the mean
%J Matematičeskie zametki
%D 1974
%P 801-811
%V 16
%N 5
%U http://geodesic.mathdoc.fr/item/MZM_1974_16_5_a14/
%G ru
%F MZM_1974_16_5_a14

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

The paper deals with approximations of a function $f$ of space $L_p[0,1]$ by rational functions in the metric of this same space ($0). It is shown that sufficiently rapid decrease as $n\to\infty$ of the least deviations $R_n(f,р)$ of function$f$ of rational functions of degree no higher than $n$ is evidence of the presence in $f$ of derivatives and differentials of a definite order if differentiation is understood as differentiation in the metric of space $L_q[0,1]$, with $0, where $q(p)$ depends on $p$ and the differentiation order, $q(p).