Geodesic
On the summability of the discrete Hilbert transform
Ural mathematical journal, Tome 4 (2018) no. 2, pp. 6-12 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In this paper, we study the asymptotic behavior of the distribution function of the discrete Hilbert transform of sequences from the class $l_1$ and find a necessary condition and a sufficient condition for the summability of the discrete Hilbert transform of a sequence from the class $l_1$.
Keywords: Discrete Hilbert transform, Asymptotic behavior of the distribution function, Class of summable sequences. 
@article{UMJ_2018_4_2_a1,
     author = {Rashid A. Aliev and Aynur F. Amrahova},
     title = {On the summability of the discrete {Hilbert} transform},
     journal = {Ural mathematical journal},
     pages = {6--12},
     year = {2018},
     volume = {4},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a1/}
}
TY  - JOUR
AU  - Rashid A. Aliev
AU  - Aynur F. Amrahova
TI  - On the summability of the discrete Hilbert transform
JO  - Ural mathematical journal
PY  - 2018
SP  - 6
EP  - 12
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a1/
LA  - en
ID  - UMJ_2018_4_2_a1
ER  - 
%0 Journal Article
%A Rashid A. Aliev
%A Aynur F. Amrahova
%T On the summability of the discrete Hilbert transform
%J Ural mathematical journal
%D 2018
%P 6-12
%V 4
%N 2
%U http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a1/
%G en
%F UMJ_2018_4_2_a1
Rashid A. Aliev; Aynur F. Amrahova. On the summability of the discrete Hilbert transform. Ural mathematical journal, Tome 4 (2018) no. 2, pp. 6-12. http://geodesic.mathdoc.fr/item/UMJ_2018_4_2_a1/

[1] Andersen K.F., “Inequalities with weights for discrete Hilbert transforms”, Canad. Math. Bul., 20 (1977), 9–16 | DOI | MR | Zbl

[2] Belov Y., Mengestie T.Y., Seip K., “Discrete Hilbert transforms on sparse sequences”, Proc. London Math. Soc., 103:1 (2011), 73–105 | DOI | MR | Zbl

[3] Belov Y., Mengestie T.Y., Seip K., “Unitary discrete Hilbert transforms”, J. Anal. Math., 112 (2010), 383–393 | DOI | MR | Zbl

[4] De Carli L., Samad S., “One-parameter groups and discrete Hilbert transform”, Canad. Math. Bull., 59 (2016), 497–507, arXiv: 506.03362 [math.FA]. 1506.03362 | DOI | MR | Zbl

[5] Gabisonija I., Meskhi A., “Two weighted inequalities for a discrete Hilbert transform”, Proc. A. Razmadze Math. Inst., 116 (1998), 107–122 http://rmi.tsu.ge/proceedings/volumes/ps/v116-4.ps.gz | MR | Zbl

[6] Hunt R., Muckenhoupt B., Wheeden R., “Weighted norm inequalities for the conjugate function and Hilbert transform”, Trans. Amer. Math. Soc., 176:2 (1973), 227–251 | DOI | MR | Zbl

[7] Laeng E., “Remarks on the Hilbert transform and some families of multiplier operators related to it”, Collect. Math., 58:1 (2007), 25–44 https://www.raco.cat/index.php/CollectaneaMathematica/article/view/57795 | MR | Zbl

[8] Liflyand E., “Weighted Estimates for the Discrete Hilbert Transform.”, Methods of Fourier Analysis and Approximation Theory. Applied and Numerical Harmonic Analysis, eds. M. Ruzhansky, S. Tikhonov. Cham: Birkhäuser, 2016, 59–69 | DOI | MR | Zbl

[9] Rakotondratsimba Y., “Two weight inequality for the discrete Hilbert transform”, Soochow J. Math., 25: 4 (1999), 353–373 http://mathlab.math.scu.edu.tw/mp/pdf/S25N44.pdf | MR | Zbl

[10] Riesz M., “Sur les fonctions conjuguees”, Math. Z., 27 (1928), 218–244 https://eudml.org/doc/167977 | DOI | MR

[11] Stepanov V.D., Tikhonov S.Yu., “Two weight inequalities for the Hilbert transform of monotone functions”, Dokl. Math., 83:2 (2011), 241–242 | DOI | MR | Zbl