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Two-sided estimates of the Lebesgue constants with respect to Vilenkin systems and applications
(Journal article; Peer reviewed; Tidsskriftartikkel, 2017-03-13)
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.