Blar i forfatter "Nadirashvili, Nato"

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    • Convergence of T means with respect to Vilenkin systems of integrable functions 

      Baramidze, Davit; Gogolashvili, Nata; Nadirashvili, Nato (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-05-06)
      In this paper, we derive the convergence of T means of Vilenkin–Fourier series with monotone coefficients of integrable functions in Lebesgue and Vilenkin–Lebesgue points. Moreover, we discuss the pointwise and norm convergence in <i><b>L</i></b><sub>p</sub> norms of such T means.

    • Some weak type inequalities and almost everywhere convergence of Vilenkin–Nörlund means 

      Baramidze, Davit; Nadirashvili, Nato; Persson, Lars-Erik; Tephnadze, George (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-05-04)
      We prove and discuss some new weak type (1, 1) inequalities of maximal operators of Vilenkin–Nörlund means generated by monotone coefficients. Moreover, we use these results to prove a.e. convergence of such Vilenkin–Nörlund means. As applications, both some well-known and new inequalities are pointed out.

    • Vilenkin–Lebesgue Points and Almost Everywhere Convergence for Some Classical Summability Methods 

      Nadirashvili, Nato; Persson, Lars-Erik; Tephnadze, George; Weisz, Ferenc (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-09-17)
      The concept of Vilenkin–Lebesgue points was introduced in [12], where the almost everywhere convergence of Fejer means of Vilenkin–Fourier series was proved. In this paper, we present a different (and simpler) approach to prove a similar result, which can be used to prove that the corresponding result holds also in a more general context, namely for regular Norlund and T-means.