Geodesic
On the uniqueness of Haar series convergent in the metrics of $L_p[0,\,1]$, $0$, and in measure
Sbornik. Mathematics, Tome 54 (1986) no. 1, pp. 99-111

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

It is established that if the partial sums $S_n(x)$ of a Haar series $\sum a_n\chi_n(x)$ converge to $f(x)\in L_p[0,1]$, $0$, at the rate $\int_0^1|S_n-f|^p\,dx=o\bigl(\frac1{n^{1-p}}\bigr)$, then $f(x)$ is $A$-integrable and $a_n=(A)\int_0^1f(x)\chi_n(x)\,dx$, for $n=1,2,\dots$. Analogous theorems are proved also for the case where Haar series converge in the metric of $L_p[0,1]$, $0$, over some subsequences of partial sums. The sharpness of these theorems is also proved. Bibliography: 10 titles. 
@article{SM_1986_54_1_a4,
     author = {A. A. Talalyan},
     title = {On the uniqueness of {Haar} series convergent in the metrics of  $L_p[0,\,1]$, $0<p<1$, and in measure},
     journal = {Sbornik. Mathematics},
     pages = {99--111},
     publisher = {mathdoc},
     volume = {54},
     number = {1},
     year = {1986},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1986_54_1_a4/}
}
TY  - JOUR
AU  - A. A. Talalyan
TI  - On the uniqueness of Haar series convergent in the metrics of  $L_p[0,\,1]$, $0
JO  - Sbornik. Mathematics
PY  - 1986
SP  - 99
EP  - 111
VL  - 54
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SM_1986_54_1_a4/
LA  - en
ID  - SM_1986_54_1_a4
ER  - 
%0 Journal Article
%A A. A. Talalyan
%T On the uniqueness of Haar series convergent in the metrics of  $L_p[0,\,1]$, $0
%J Sbornik. Mathematics
%D 1986
%P 99-111
%V 54
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SM_1986_54_1_a4/
%G en
%F SM_1986_54_1_a4
A. A. Talalyan. On the uniqueness of Haar series convergent in the metrics of  $L_p[0,\,1]$, $0