Blar i forfatter "Baramidze, Davit"

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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.

    • SHARP (Hp, Lp) AND (Hp, weak − Lp) TYPE INEQUALITIES OF WEIGHTED MAXIMAL OPERATORS OF T MEANS WITH RESPECT TO VILENKIN SYSTEMS 

      Baramidze, Davit (Journal article; Tidsskriftartikkel; Peer reviewed, 2022)
      We discuss (Hp, Lp) and (Hp, weak − Lp) type inequalities of weighted maximal operators of T means with respect to the Vilenkin systems with monotone coefficients [44] and prove that these results are the best possible in a special sense. As applications, both some well-known and new results are pointed out.

    • Some new (Hp – Lp) type inequalities for weighted maximal operators of partial sums of Walsh–Fourier series 

      Baramidze, Davit; Persson, Lars-Erik; Tephnadze, George (Journal article; Tidsskriftartikkel, 2023-05-16)
      In this paper we introduce some new weighted maximal operators of the partial sums of the Walsh–Fourier series. We prove that for some “optimal” weights these new operators indeed are bounded from the martingale Hardy space <i>H<sub>p</sub>(G)</i> to the Lebesgue space <i>L<sub>p</sub>(G)</i>, for 0&#60;p&#60;1. Moreover, we also prove sharpness of this result. As a consequence we obtain some new ...

    • Some new restricted maximal operators of Fejér means of Walsh–Fourier series 

      Baramidze, Davit; Baramidze, Lasha; Perssson, Lars-Erik; Tephnadze, George (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-09-12)

    • Some new restricted maximal operators of Fejér means of Walsh–Fourier series 

      Baramidze, Davit; Baramidze, Lasha; Persson, Lars-Erik; Tephnadze, George (Journal article; Tidsskriftartikkel, 2023-09-12)
      In this paper, we derive the maximal subspace of natural numbers { <i>n<sub>k</sub></i> : <i>k</i> &#8805; 0 }, such that the restricted maximal operator, defined by sup<sub><i>k</i>&#8712;&#8469;</sub> | &sigma;<i><sub>n<sub>k</sub></sub>F</i> | on this subspace of Fejér means of Walsh–Fourier series is bounded from the martingale Hardy space <i>H</i><sub>1/2</sub> to the Lebesgue space ...

    • Some New weak-(Hp-Lp) Type Inequalities For Weighted Maximal Operators Of Fejér Means Of Walsh–Fourier Series 

      Baramidze, Davit; Tephnadze, G. (Journal article; Tidsskriftartikkel; Peer reviewed, 2023-12-13)
      We introduce some new weighted maximal operators of the Fejér means of the Walsh–Fourier series. We prove that for some "optimal" weights these new operators are bounded from the martingale Hardy space H<sub>p</sub>(G) to the space weak-L<sub>p</sub>(G), for 0 <p<1/2. Moreover, we also prove sharpness of this result. As a consequence we obtain some new and well-known results.

    • 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.