Geodesic
On Weyl multipliers of the rearranged trigonometric system
Sbornik. Mathematics, Tome 211 (2020) no. 12, pp. 1704-1736

Voir la notice de l'article provenant de la source Math-Net.Ru

We prove that the condition $\sum_{n=1}^\infty1/(nw(n))\infty$ is necessary for an increasing sequence of numbers $w(n)$ to be an almost everywhere unconditional convergence Weyl multiplier for the trigonometric system. This property was known long ago for Haar, Walsh, Franklin and some other classical orthogonal systems. The proof of this result is based on a new sharp logarithmic lower bound on $L^2$ for the majorant operator related to the rearranged trigonometric system. Bibliography: 32 titles.
Keywords: trigonometric series, Menshov-Rademacher theorem.
Mots-clés : Weyl multiplier 
@article{SM_2020_211_12_a1,
     author = {G. A. Karagulyan},
     title = {On {Weyl} multipliers of the rearranged trigonometric system},
     journal = {Sbornik. Mathematics},
     pages = {1704--1736},
     publisher = {mathdoc},
     volume = {211},
     number = {12},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2020_211_12_a1/}
}
TY  - JOUR
AU  - G. A. Karagulyan
TI  - On Weyl multipliers of the rearranged trigonometric system
JO  - Sbornik. Mathematics
PY  - 2020
SP  - 1704
EP  - 1736
VL  - 211
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_2020_211_12_a1/
LA  - en
ID  - SM_2020_211_12_a1
ER  - 
%0 Journal Article
%A G. A. Karagulyan
%T On Weyl multipliers of the rearranged trigonometric system
%J Sbornik. Mathematics
%D 2020
%P 1704-1736
%V 211
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_2020_211_12_a1/
%G en
%F SM_2020_211_12_a1
G. A. Karagulyan. On Weyl multipliers of the rearranged trigonometric system. Sbornik. Mathematics, Tome 211 (2020) no. 12, pp. 1704-1736. http://geodesic.mathdoc.fr/item/SM_2020_211_12_a1/