The Hardy--Littlewood Theorem for Multiple Fourier Series with Monotone Coefficients
Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 502-510
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It was proved earlier that, for multiple Fourier series whose coefficients are monotone in each index, the classical Hardy–Littlewood theorem is not valid for $p\le 2m/(m+1)$, where $m$ is the dimension of the space. We establish how the theorem must be modified in this case.
Keywords:
Hardy–Littlewood theorem, multiple Fourier series, trigonometric polynomial.
@article{MZM_2016_99_4_a2,
author = {M. I. Dyachenko and E. D. Nursultanov and M. E. Nursultanov},
title = {The {Hardy--Littlewood} {Theorem} for {Multiple} {Fourier} {Series} with {Monotone} {Coefficients}},
journal = {Matemati\v{c}eskie zametki},
pages = {502--510},
publisher = {mathdoc},
volume = {99},
number = {4},
year = {2016},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a2/}
}
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M. I. Dyachenko; E. D. Nursultanov; M. E. Nursultanov. The Hardy--Littlewood Theorem for Multiple Fourier Series with Monotone Coefficients. Matematičeskie zametki, Tome 99 (2016) no. 4, pp. 502-510. http://geodesic.mathdoc.fr/item/MZM_2016_99_4_a2/