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Matematicheskie Zametki, 2016, Volume 99, Issue 4, Pages 502–510
DOI: https://doi.org/10.4213/mzm10844 (Mi mzm10844) 		 
This article is cited in 2 scientific papers (total in 2 papers)

The Hardy–Littlewood Theorem for Multiple Fourier Series with Monotone Coefficients

M. I. Dyachenkoa, E. D. Nursultanovb, M. E. Nursultanovb

a Lomonosov Moscow State University
b L. N. Gumilev Eurasian National University, Astana
Full-text PDF (495 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10844
Abstract: 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.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-01236
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
Ministry of Education and Science of the Republic of Kazakhstan 4080/ГФ4
3311/ГФ4
The work of the first author was supported by the Russian Foundation for Basic Research under grant 15-01-01236 and by the program “Leading Scientific Schools” under grant NSh-3682.2014.1. The work of the second author was supported by the Ministry of Education and Science of the Republic of Kazakhstan under grants 4080/GF4 and 3311/GF4.
Received: 16.04.2015
Revised: 23.10.2015
English version:
Mathematical Notes, 2016, Volume 99, Issue 4, Pages 503–510
DOI: https://doi.org/10.1134/S0001434616030238
Bibliographic databases:
Document Type: Article
UDC: 517.52
Language: Russian
Citation: M. I. Dyachenko, E. D. Nursultanov, M. E. Nursultanov, “The Hardy–Littlewood Theorem for Multiple Fourier Series with Monotone Coefficients”, Mat. Zametki, 99:4 (2016), 502–510; Math. Notes, 99:4 (2016), 503–510
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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