Geodesic
TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS
Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 17-34

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DOI

In this paper, we derive two-sided estimates of the Lebesgue constants for bounded Vilenkin systems, we also present some applications of importance, e.g., we obtain a characterization for the boundedness of a subsequence of partial sums with respect to Vilenkin–Fourier series of H 1 martingales in terms of n's variation. The conditions given in this paper are in a sense necessary and sufficient. 
BLAHOTA, I.; PERSSON, L. E.; TEPHNADZE, G. TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS. Glasgow mathematical journal, Tome 60 (2018) no. 1, pp. 17-34. doi: 10.1017/S0017089516000549
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     author = {BLAHOTA, I. and PERSSON, L. E. and TEPHNADZE, G.},
     title = {TWO-SIDED {ESTIMATES} {OF} {THE} {LEBESGUE} {CONSTANTS} {WITH} {RESPECT} {TO} {VILENKIN} {SYSTEMS} {AND} {APPLICATIONS}},
     journal = {Glasgow mathematical journal},
     pages = {17--34},
     year = {2018},
     volume = {60},
     number = {1},
     doi = {10.1017/S0017089516000549},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089516000549/}
}
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%A PERSSON, L. E.
%A TEPHNADZE, G.
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