Geodesic
Concerning a sufficient condition of Sidon for the integrability of trigonometric series
Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 317-328 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider problems concerning integrability and convergence in the metric $L$ of trigonometric series, the coefficients $a_k$ of which satisfy the conditions: $a_k\to0$, there exist numbers $A_k$ such that $A_k\downarrow0$, $\sum A_k<\infty$, and $|\Delta a_k|\le A_k$. The integrability of a series in cosines under these conditions is equivalent to a theorem of Sidon. 
@article{MZM_1973_14_3_a1,
     author = {S. A. Telyakovskii},
     title = {Concerning a sufficient condition of {Sidon} for the integrability of trigonometric series},
     journal = {Matemati\v{c}eskie zametki},
     pages = {317--328},
     year = {1973},
     volume = {14},
     number = {3},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/}
}
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S. A. Telyakovskii. Concerning a sufficient condition of Sidon for the integrability of trigonometric series. Matematičeskie zametki, Tome 14 (1973) no. 3, pp. 317-328. http://geodesic.mathdoc.fr/item/MZM_1973_14_3_a1/