Geodesic
On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 347-369

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

This paper establishes best possible conditions, on the degree of approximation of functions $f(x_1,\dots,x_m)$ in $L_p([0,1]^m)$ ($0$) by rational functions, that guarantee that the function $f$ has a $p$th mean differential of order $\lambda>0$ everywhere except on a set of zero Hausdorff ($m-1+\alpha$) measure ($0\alpha\leqslant1$). Bibliography: 11 titles. 
@article{IM2_1986_26_2_a5,
     author = {E. A. Sevast'yanov},
     title = {On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions},
     journal = {Izvestiya. Mathematics },
     pages = {347--369},
     publisher = {mathdoc},
     volume = {26},
     number = {2},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/}
}
TY  - JOUR
AU  - E. A. Sevast'yanov
TI  - On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
JO  - Izvestiya. Mathematics 
PY  - 1986
SP  - 347
EP  - 369
VL  - 26
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/
LA  - en
ID  - IM2_1986_26_2_a5
ER  - 
%0 Journal Article
%A E. A. Sevast'yanov
%T On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions
%J Izvestiya. Mathematics 
%D 1986
%P 347-369
%V 26
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/
%G en
%F IM2_1986_26_2_a5
E. A. Sevast'yanov. On~an~estimate for the smallness of sets of points of nondifferentiability of functions as related to the degree of approximation by rational functions. Izvestiya. Mathematics , Tome 26 (1986) no. 2, pp. 347-369. http://geodesic.mathdoc.fr/item/IM2_1986_26_2_a5/