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
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.
@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
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/