Geodesic
On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative
Eurasian mathematical journal, Tome 9 (2018) no. 2, pp. 11-21

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

A new non-periodic modulus of smoothness related to the Riesz derivative is constructed. Its properties are studied in the spaces $L_p(\mathbb{R})$ of non-periodic functions with $1\leqslant p\leqslant+\infty$. The direct Jackson type estimate is proved. It is shown that the introduced modulus is equivalent to the $K$-functional related to the Riesz derivative and to the approximation error of the convolution integrals generated by the Fejér kernel. 
@article{EMJ_2018_9_2_a2,
     author = {S. Yu. Artamonov},
     title = {On some constructions of a non-periodic modulus of smoothness related to the {Riesz} derivative},
     journal = {Eurasian mathematical journal},
     pages = {11--21},
     publisher = {mathdoc},
     volume = {9},
     number = {2},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EMJ_2018_9_2_a2/}
}
TY  - JOUR
AU  - S. Yu. Artamonov
TI  - On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative
JO  - Eurasian mathematical journal
PY  - 2018
SP  - 11
EP  - 21
VL  - 9
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/EMJ_2018_9_2_a2/
LA  - en
ID  - EMJ_2018_9_2_a2
ER  - 
%0 Journal Article
%A S. Yu. Artamonov
%T On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative
%J Eurasian mathematical journal
%D 2018
%P 11-21
%V 9
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/EMJ_2018_9_2_a2/
%G en
%F EMJ_2018_9_2_a2
S. Yu. Artamonov. On some constructions of a non-periodic modulus of smoothness related to the Riesz derivative. Eurasian mathematical journal, Tome 9 (2018) no. 2, pp. 11-21. http://geodesic.mathdoc.fr/item/EMJ_2018_9_2_a2/