Geodesic
On Uniformly Convergent Rearrangements of Trigonometric Fourier Series
Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 80-87

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We show that if the module of continuity $\omega(f,\delta)$ of a $2\pi$-periodic function $f\in C(\mathbb T)$ is $o(1/\log\log1/\delta)$ as $\delta\to0+$ then there exists a rearrangement of the trigonometric Fourier series of $f$ converging uniformly to $f$. 
@article{CMFD_2007_25_a6,
     author = {S. V. Konyagin},
     title = {On {Uniformly} {Convergent} {Rearrangements} of {Trigonometric} {Fourier} {Series}},
     journal = {Contemporary Mathematics. Fundamental Directions},
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     year = {2007},
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     url = {http://geodesic.mathdoc.fr/item/CMFD_2007_25_a6/}
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S. V. Konyagin. On Uniformly Convergent Rearrangements of Trigonometric Fourier Series. Contemporary Mathematics. Fundamental Directions, Theory of functions, Tome 25 (2007), pp. 80-87. http://geodesic.mathdoc.fr/item/CMFD_2007_25_a6/