Now showing items 1-2 of 2
Some inequalities for Cesàro means of double Vilenkin-Fourier series
(Journal article; Peer reviewed; Tidsskriftartikkel, 2018-12-19)
In this paper, we state and prove some new inequalities related to the rate of Lp approximation by Cesàro means of the quadratic partial sums of double Vilenkin–Fourier series of functions from Lp.
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.