Geodesic
Note on estimates for the growth order of sequences of multiple rectangular Fourier sums
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 55-59
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

Let $\{S_{\mathbf n_k}(f,\mathbf x)\}_{k=1}^\infty$ be some sequence of rectangular partial sums of the multiple trigonometric Fourier series of a function $f$, and let $\{\lambda_k\}_{k=1}^\infty$ be a nondecreasing sequence of positive numbers. We investigate conditions on the belonging of the function $f$ to the classes $\varphi (L)$ under which estimates of the following form are possible: $$ S_{\mathbf n_k}(f,\mathbf x)=o(\lambda_k )\quad\text{a.e.} $$ where the right-hand side depends on $k$ only.
Keywords: multiple trigonometric Fourier series, growth order estimates. 
@article{TIMM_2011_17_3_a7,
     author = {N. Yu. Antonov},
     title = {Note on estimates for the growth order of sequences of multiple rectangular {Fourier} sums},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {55--59},
     year = {2011},
     volume = {17},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a7/}
}
TY  - JOUR
AU  - N. Yu. Antonov
TI  - Note on estimates for the growth order of sequences of multiple rectangular Fourier sums
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2011
SP  - 55
EP  - 59
VL  - 17
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a7/
LA  - ru
ID  - TIMM_2011_17_3_a7
ER  - 
%0 Journal Article
%A N. Yu. Antonov
%T Note on estimates for the growth order of sequences of multiple rectangular Fourier sums
%J Trudy Instituta matematiki i mehaniki
%D 2011
%P 55-59
%V 17
%N 3
%U http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a7/
%G ru
%F TIMM_2011_17_3_a7
N. Yu. Antonov. Note on estimates for the growth order of sequences of multiple rectangular Fourier sums. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 3, pp. 55-59. http://geodesic.mathdoc.fr/item/TIMM_2011_17_3_a7/

[1] Hardy G. H., “On the summability of Fourier series”, Proc. London Math. Soc., 12 (1913), 365–372 | Zbl

[2] Oskolkov K. I., “Podposledovatelnosti summ Fure integriruemykh funktsii”, Tr. MIAN, 167, 1985, 239–260 | MR | Zbl

[3] Karagulyan G. A., “Preobrazovanie Gilberta i eksponentsialnye integralnye otsenki pryamougolnykh chastichnykh summ dvoinykh ryadov Fure”, Mat. sb., 187:3 (1996), 55–74 | MR | Zbl

[4] Antonov N. Yu., “O skorosti rosta proizvolnykh posledovatelnostei dvoinykh pryamougolnykh summ Fure”, Trudy Instituta matematiki i mekhaniki UrO RAN, 16, no. 4, 2010, 31–37

[5] Antonov N. Yu., “O skorosti rosta posledovatelnostei kratnykh pryamougolnykh summ Fure”, Trudy Instituta matematiki i mekhaniki UrO RAN, 11, no. 2, 2005, 10–29 | MR | Zbl

[6] Konyagin S. V., “O perestanovkakh funktsii i raskhodimosti ryadov Fure po kubam”, Tr. MIAN, 189, 1989, 98–109 | MR | Zbl

[7] Getsadze R. D., “O raskhodimosti po mere kratnykh ryadov Fure”, Soobsch. AN Gruzinskoi SSR, 122:2 (1986), 269–271 | MR

[8] Getsadze R. D., “O raskhodimosti po mere kratnykh ryadov Fure”, Nekotorye voprosy teorii funktsii i funktsionalnogo analiza, v. 4, Izd-vo Tbil. un-ta, Tbilisi, 1988, 59–76

[9] Antonov N. Yu., “O skhodimosti pochti vsyudu po kubam kratnykh trigonometricheskikh ryadov Fure”, Izv. RAN. Ser. mat., 68:2 (2004), 3–22 | MR | Zbl

[10] Stein E. M., “On limits of sequences of operators”, Ann. Math., 74:1 (1961), 140–170 | DOI | MR | Zbl