Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 67-75
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S. V. Kislyakov. A correction theorem and the dyadic space $H(1,\infty)$. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 67-75. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a4/
@article{ZNSL_1986_149_a4,
author = {S. V. Kislyakov},
title = {A correction theorem and the dyadic space~$H(1,\infty)$},
journal = {Zapiski Nauchnykh Seminarov POMI},
pages = {67--75},
year = {1986},
volume = {149},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a4/}
}
TY - JOUR
AU - S. V. Kislyakov
TI - A correction theorem and the dyadic space $H(1,\infty)$
JO - Zapiski Nauchnykh Seminarov POMI
PY - 1986
SP - 67
EP - 75
VL - 149
UR - http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a4/
LA - ru
ID - ZNSL_1986_149_a4
ER -
%0 Journal Article
%A S. V. Kislyakov
%T A correction theorem and the dyadic space $H(1,\infty)$
%J Zapiski Nauchnykh Seminarov POMI
%D 1986
%P 67-75
%V 149
%U http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a4/
%G ru
%F ZNSL_1986_149_a4
It is proved that for every $L^\infty$-function $f$ and positive $\varepsilon$ there is a function $g$ whose partial sums of both Fourier and Walsh–Fourier series are uniformly bounded by $c(\log 1/\varepsilon)\|f\|_\infty$ and that satisfies $\operatorname{mes}\{f\ne g\}<\varepsilon$.
