Growth estimates for arbitrary sequences of multiple rectangular Fourier sums
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 26-33
Cet article a éte moissonné depuis la source Math-Net.Ru
Growth estimates are obtained on a set of full measure for arbitrary sequences of rectangular partial sums of multiple trigonometric Fourier sums.
Keywords:
trigonometric Fourier series, growth order almost everywhere.
@article{TIMM_2013_19_2_a2,
author = {N. Yu. Antonov},
title = {Growth estimates for arbitrary sequences of multiple rectangular {Fourier} sums},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {26--33},
year = {2013},
volume = {19},
number = {2},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a2/}
}
N. Yu. Antonov. Growth estimates for arbitrary sequences of multiple rectangular Fourier sums. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 19 (2013) no. 2, pp. 26-33. http://geodesic.mathdoc.fr/item/TIMM_2013_19_2_a2/
[1] Hardy G. H., “On the summability of Fourier series”, Proc. London Math. Soc., 12 (1913), 365–372 | DOI | 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 | DOI | MR | Zbl
[4] Antonov N. Yu., “O poryadke rosta posledovatelnostei dvoinykh pryamougolnykh summ Fure funktsii iz klassov $\varphi(L)$”, Tr. In-ta matematiki i mekhaniki UrO RAN, 18, no. 4, 2012, 26–34
[5] Stein E. M., “On limits of sequences of operators”, Ann. Math., 74:1 (1961), 140–170 | DOI | MR | Zbl