Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1003-1013
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M. I. Dyachenko. The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 5 (1999) no. 4, pp. 1003-1013. http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a3/
@article{FPM_1999_5_4_a3,
author = {M. I. Dyachenko},
title = {The~rate of {Pringsheim} convergence of multiple {Fourier} series of piecewise monotonic functions of many variables in the~space~$L$},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {1003--1013},
year = {1999},
volume = {5},
number = {4},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a3/}
}
TY - JOUR
AU - M. I. Dyachenko
TI - The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$
JO - Fundamentalʹnaâ i prikladnaâ matematika
PY - 1999
SP - 1003
EP - 1013
VL - 5
IS - 4
UR - http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a3/
LA - ru
ID - FPM_1999_5_4_a3
ER -
%0 Journal Article
%A M. I. Dyachenko
%T The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 1999
%P 1003-1013
%V 5
%N 4
%U http://geodesic.mathdoc.fr/item/FPM_1999_5_4_a3/
%G ru
%F FPM_1999_5_4_a3
It has been earlier proved by the author that the Fourier series of piecewise monotonic functions of many variables converge in the sense of Pringsheim pointwise and in $C(T^m)$-metric faster than in the case of arbitrary continuous functions. The main result of the paper says that this is not valid for the Pringsheim convergence in $L(T^m)$-metric.
