Abstract
We show that if the module of continuity ω(ƒ, δ) of a 2π-periodic function ƒ ∈ {ie081-01} is o(1/ log log 1/δ) as δ → 0+, then there exists a rearrangement of the trigonometric Fourier series of ƒ converging uniformly to ƒ.
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Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.
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Konyagin, S.V. On uniformly convergent rearrangements of trigonometric Fourier series. J Math Sci 155, 81–88 (2008). https://doi.org/10.1007/s10958-008-9209-x
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DOI: https://doi.org/10.1007/s10958-008-9209-x