Blar i forfatter "Tephnadze, G."

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    • An Analogy of the Carleson–Hunt Theorem with Respect to Vilenkin Systems 

      Persson, Lars-Erik; Schipp, F.; Tephnadze, G.; Weisz, F. (Journal article; Tidsskriftartikkel; Peer reviewed, 2022-05-13)
      In this paper we discuss and prove an analogy of the Carleson–Hunt theorem with respect to Vilenkin systems. In particular, we use the theory of martingales and give a new and shorter proof of the almost everywhere convergence of Vilenkin–Fourier series of f ∈ L <sub>p</sub>(G<sub>m</sub>)for p > 1 in case the Vilenkin system is bounded. Moreover, we also prove sharpness by stating an analogy of the ...

    • 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.