Geodesic
Some convergence tests for Fourier series with respect to Vilenkin system in the case of unbounded $p_k$
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 42-44

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Series with respect to a system of characters of a zero-dimensional compact commutative group are considered. A generalization of the analogue of Dini test and its corollary obtained earlier for systems determined by bounded sequencees $\{p_k\}$ are proved. 
@article{VMUMM_2019_5_a6,
     author = {S. M. Voronov},
     title = {Some convergence tests for {Fourier} series with respect to {Vilenkin} system in the case of unbounded $p_k$},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {42--44},
     publisher = {mathdoc},
     number = {5},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a6/}
}
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%F VMUMM_2019_5_a6
S. M. Voronov. Some convergence tests for Fourier series with respect to Vilenkin system in the case of unbounded $p_k$. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2019), pp. 42-44. http://geodesic.mathdoc.fr/item/VMUMM_2019_5_a6/