Geodesic
Convergence and divergence systems
Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 253-260.

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A generalization of Carleson's theorem concerning series with respect to systems $\{\varphi(nx)\}$ is proved for the case in which $\varphi(x)$ can be expanded in an absolutely convergent Fourier series. Systems corresponding to functions $\varphi(x)$ which have lacunary Fourier series are studied in detail. 
@article{MZM_1968_4_3_a0,
     author = {V. F. Gaposhkin},
     title = {Convergence and divergence systems},
     journal = {Matemati\v{c}eskie zametki},
     pages = {253--260},
     publisher = {mathdoc},
     volume = {4},
     number = {3},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a0/}
}
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V. F. Gaposhkin. Convergence and divergence systems. Matematičeskie zametki, Tome 4 (1968) no. 3, pp. 253-260. http://geodesic.mathdoc.fr/item/MZM_1968_4_3_a0/