Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications
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.
Accepted manuscript version. Published version available at https://doi.org/10.1017/S0017089516000549