Geodesic
Exact inequalities for splines and best quadrature formulas for certain classes of functions
Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 913-926 
A. A. Ligun. Exact inequalities for splines and best quadrature formulas for certain classes of functions. Matematičeskie zametki, Tome 19 (1976) no. 6, pp. 913-926. http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a10/
@article{MZM_1976_19_6_a10,
     author = {A. A. Ligun},
     title = {Exact inequalities for splines and best quadrature formulas for certain classes of functions},
     journal = {Matemati\v{c}eskie zametki},
     pages = {913--926},
     year = {1976},
     volume = {19},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a10/}
}
TY  - JOUR
AU  - A. A. Ligun
TI  - Exact inequalities for splines and best quadrature formulas for certain classes of functions
JO  - Matematičeskie zametki
PY  - 1976
SP  - 913
EP  - 926
VL  - 19
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a10/
LA  - ru
ID  - MZM_1976_19_6_a10
ER  - 
%0 Journal Article
%A A. A. Ligun
%T Exact inequalities for splines and best quadrature formulas for certain classes of functions
%J Matematičeskie zametki
%D 1976
%P 913-926
%V 19
%N 6
%U http://geodesic.mathdoc.fr/item/MZM_1976_19_6_a10/
%G ru
%F MZM_1976_19_6_a10

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

In this note inequalities between the norms of a spline and its derivatives in various Orlich spaces are obtained. These inequalities are analogs of the inequalities of L. V. Takov for trigonometrical polynomials and generalize S. N. Bernstein's inequalities. An inequality for monosplines which reduces to the best quadrature formula for the classes $W^rL_1$, where $r=1,2,\dots$, is also obtained. For $r=2,4,6,\dots$ this result was obtained earlier by V. P. Motornyi.