Geodesic
Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables
Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 369-403

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

The author studies the magnitudes of the suprema of the deviations of rectangular Fourier sums on classes of continuous periodic functions determined by arbitrary partial moduli of continuity. Order precise upper estimates for these magnitudes are found, and in the case where the moduli of continuity are convex asymptotic equalities are obtained that are full analogues of the corresponding one-dimensional equalities of A. N. Kolmogorov and S. M. Nikol'skii. Bibliography: 12 titles. 
@article{IM2_1981_17_2_a7,
     author = {A. I. Stepanets},
     title = {Estimates of the deviations of partial {Fourier} sums on classes of continuous periodic functions of several variables},
     journal = {Izvestiya. Mathematics },
     pages = {369--403},
     publisher = {mathdoc},
     volume = {17},
     number = {2},
     year = {1981},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a7/}
}
TY  - JOUR
AU  - A. I. Stepanets
TI  - Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables
JO  - Izvestiya. Mathematics 
PY  - 1981
SP  - 369
EP  - 403
VL  - 17
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a7/
LA  - en
ID  - IM2_1981_17_2_a7
ER  - 
%0 Journal Article
%A A. I. Stepanets
%T Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables
%J Izvestiya. Mathematics 
%D 1981
%P 369-403
%V 17
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a7/
%G en
%F IM2_1981_17_2_a7
A. I. Stepanets. Estimates of the deviations of partial Fourier sums on classes of continuous periodic functions of several variables. Izvestiya. Mathematics , Tome 17 (1981) no. 2, pp. 369-403. http://geodesic.mathdoc.fr/item/IM2_1981_17_2_a7/