FPM 1999, vol. 5, no. 4, pp. 1003-1013

FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1999, VOLUME 5, NUMBER 4, PAGES 1003-1013

The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$

M. I. Dyachenko

Abstract

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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.

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The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space L

The rate of Pringsheim convergence of multiple Fourier series of piecewise monotonic functions of many variables in the space $L$