On uniformly convergent rearrangements of trigonometric Fourier series

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. __________ Translated from Sovremennaya Matematika. Fundamental'nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 25, Theory of Functions, 2007.