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The Hardy–Littlewood theorem for multiple fourier series with monotone coefficients

Authors
  • D’yachenko, M. I.1
  • Nursultanov, E. D.2
  • Nursultanov, M. E.2
  • 1 Lomonosov Moscow State University, Moscow, Russia , Moscow (Russia)
  • 2 Gumilev Eurasian National University, Astana, Kazakhstan , Astana (Kazakhstan)
Type
Published Article
Journal
Mathematical Notes
Publisher
Pleiades Publishing
Publication Date
Mar 01, 2016
Volume
99
Issue
3-4
Pages
503–510
Identifiers
DOI: 10.1134/S0001434616030238
Source
Springer Nature
Keywords
License
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Abstract

It was proved earlier that, for multiple Fourier series whose coefficients are monotone in each index, the classicalHardy–Littlewood theorem is not valid for p ≤ 2m/(m+1), where m is the dimension of the space. We establish how the theorem must be modified in this case.

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