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arXiv · 2509.19321

Maximal operators of $T$ means with respect to the Vilenkin system

G. Tutberidze
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Abstract

In this paper we prove and discuss some new $\left( H_{p},weak-L_{p}\right) $ type inequalities of maximal operators of $T$ means with respect to Vilenkin systems with monotone coefficients. We also apply these results to prove a.e. convergence of \ such $T$ means. It has also been proven that these results are the best possible in a special sense. As applications, both well-known and new results are highlighted.

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G. Tutberidze. 2025-09-12. Maximal operators of $T$ means with respect to the Vilenkin system. https://arxiv.org/abs/2509.19321

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