, Volume 155, Issue 1, pp 81-88
Date: 31 Oct 2008

On uniformly convergent rearrangements of trigonometric Fourier series

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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.