Now showing items 1-3 of 3

    • Sharp Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications 

      Baramidze, Lasha; Persson, Lars Erik; Tephnadze, G; Wall, P (Peer reviewed, 2016-10-01)
      We prove and discuss some new Hp-Lp type inequalities of weighted maximal operators of Vilenkin-Nörlund means with monotone coefficients. It is also proved that these inequalities are the best possible in a special sense. We also apply these results to prove strong summability for such Vilenkin-Nörlund means. As applications, both some well-known and new results are pointed out.
    • Some inequalities for Cesàro means of double Vilenkin-Fourier series 

      Tephnadze, G; Persson, Lars Erik (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 

      Blahota, Istvan; Persson, Lars Erik; Tephnadze, G (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.