Now showing items 1-2 of 2
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.
A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces
(Journal article; Peer reviewed, 2018-09-20)
The restricted maximal operators of partial sums with respect to bounded Vilenkin systems are investigated. We derive the maximal subspace of positive numbers, for which this operator is bounded from the Hardy space H p to the Lebesgue space L p for all 0<p≤1 . We also prove that the result is sharp in a particular sense.