Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 393-404
Citer cet article
L. A. Shaginyan. Summability of series with respect to a Haar system by the $(C,1)$ method. Matematičeskie zametki, Tome 15 (1974) no. 3, pp. 393-404. http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/
@article{MZM_1974_15_3_a5,
author = {L. A. Shaginyan},
title = {Summability of series with respect to {a~Haar} system by the $(C,1)$ method},
journal = {Matemati\v{c}eskie zametki},
pages = {393--404},
year = {1974},
volume = {15},
number = {3},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/}
}
TY - JOUR
AU - L. A. Shaginyan
TI - Summability of series with respect to a Haar system by the $(C,1)$ method
JO - Matematičeskie zametki
PY - 1974
SP - 393
EP - 404
VL - 15
IS - 3
UR - http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/
LA - ru
ID - MZM_1974_15_3_a5
ER -
%0 Journal Article
%A L. A. Shaginyan
%T Summability of series with respect to a Haar system by the $(C,1)$ method
%J Matematičeskie zametki
%D 1974
%P 393-404
%V 15
%N 3
%U http://geodesic.mathdoc.fr/item/MZM_1974_15_3_a5/
%G ru
%F MZM_1974_15_3_a5
For a Haar-system series we prove that if the lower bound of the $(C,1)$ means of the series is larger than $-\infty$ on a set $E$ of positive measure, then the series converges to a finite function almost everywhere on $E$; from this it follows that Haar-system series are not summable by the $(C,1)$ method to $+\infty$ on sets of positive measure.
