Geodesic
On the series of absolute values of blocks of trigonometric series
Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 243-251 
S. A. Telyakovskii. On the series of absolute values of blocks of trigonometric series. Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 243-251. http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a16/
@article{TRSPY_2014_284_a16,
     author = {S. A. Telyakovskii},
     title = {On the series of absolute values of blocks of trigonometric series},
     journal = {Informatics and Automation},
     pages = {243--251},
     year = {2014},
     volume = {284},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a16/}
}
TY  - JOUR
AU  - S. A. Telyakovskii
TI  - On the series of absolute values of blocks of trigonometric series
JO  - Informatics and Automation
PY  - 2014
SP  - 243
EP  - 251
VL  - 284
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a16/
LA  - ru
ID  - TRSPY_2014_284_a16
ER  - 
%0 Journal Article
%A S. A. Telyakovskii
%T On the series of absolute values of blocks of trigonometric series
%J Informatics and Automation
%D 2014
%P 243-251
%V 284
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a16/
%G ru
%F TRSPY_2014_284_a16

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

Conditions of integrability with a power weight are obtained for the sums of series of absolute values of blocks of sine series and cosine series under certain special conditions imposed on the coefficients of these series.

[1] Telyakovskii S.A., “O chastnykh summakh ryadov Fure funktsii ogranichennoi variatsii”, Tr. MIAN, 219, 1997, 378–386 | MR

[2] Telyakovskii S.A., “Certain properties of Fourier series of functions with bounded variation”, East J. Approx., 10:1–2 (2004), 215–218 | MR | Zbl

[3] Trigub R.M., “A note on the paper of Telyakovskii “Certain properties of Fourier series of functions with bounded variation””, East J. Approx., 13:1 (2007), 1–6 | MR

[4] Belov A.S., “O summe modulei chlenov sgruppirovannogo trigonometricheskogo ryada s monotonnymi koeffitsientami”, Vestn. Ivanov. gos. un-ta. Biologiya. Khimiya. Fizika. Matematika, 2006, no. 3, 107–121

[5] Belov A.S., “O svoistvakh summy modulei chlenov sgruppirovannogo trigonometricheskogo ryada”, Mat. sb., 203:6 (2012), 35–62 | DOI | MR | Zbl

[6] Telyakovskii S.A., “O svoistvakh blokov chlenov ryada $\sum \frac 1k\sin kx$”, Ukr. mat. zhurn., 64:5 (2012), 713–718 | MR | Zbl

[7] Telyakovskii S.A., “O svoistvakh modulei blokov chlenov ryada $\sum \frac 1k\sin kx$”, Izv. Saratov. un-ta. Matematika, Mekhanika, Informatika, 13:1, Ch. 2 (2013), 92–95 | MR | Zbl