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

M. I. D’yachenko; E. D. Nursultanov; M. E. Nursultanov

doi:10.1134/S0001434616030238

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
Affiliations:
1. Lomonosov Moscow State University
2. Gumilev Eurasian National University
Issue: Vol 99, No 3-4 (2016)
Pages: 503-510
Section: Article
URL: https://journals.rcsi.science/0001-4346/article/view/149274
DOI: https://doi.org/10.1134/S0001434616030238
ID: 149274

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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.