On the growth order of sequences of double rectangular Fourier sums for functions from the classes~$\varphi(L)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 26-34
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We obtain estimates for the growth order of arbitrary sequences of rectangular partial sums of double trigonometric Fourier series for functions from the classes $\varphi(L)$, which are intermediate between $L\log^+L_{[0,2\pi)^2}$; and $L(\log^+L)^2_{[0,2\pi)^2}$.
Keywords:
multiple trigonometric Fourier series, growth order estimates.
@article{TIMM_2012_18_4_a2,
author = {N. Yu. Antonov},
title = {On the growth order of sequences of double rectangular {Fourier} sums for functions from the classes~$\varphi(L)$},
journal = {Trudy Instituta matematiki i mehaniki},
pages = {26--34},
publisher = {mathdoc},
volume = {18},
number = {4},
year = {2012},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a2/}
}
TY - JOUR AU - N. Yu. Antonov TI - On the growth order of sequences of double rectangular Fourier sums for functions from the classes~$\varphi(L)$ JO - Trudy Instituta matematiki i mehaniki PY - 2012 SP - 26 EP - 34 VL - 18 IS - 4 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a2/ LA - ru ID - TIMM_2012_18_4_a2 ER -
%0 Journal Article %A N. Yu. Antonov %T On the growth order of sequences of double rectangular Fourier sums for functions from the classes~$\varphi(L)$ %J Trudy Instituta matematiki i mehaniki %D 2012 %P 26-34 %V 18 %N 4 %I mathdoc %U http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a2/ %G ru %F TIMM_2012_18_4_a2
N. Yu. Antonov. On the growth order of sequences of double rectangular Fourier sums for functions from the classes~$\varphi(L)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 18 (2012) no. 4, pp. 26-34. http://geodesic.mathdoc.fr/item/TIMM_2012_18_4_a2/