In this paper we prove and discuss some new (Hp,weak−Lp) 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.
@article{arxiv.2509.19321,
title = {Maximal operators of $T$ means with respect to the Vilenkin system},
author = {G. Tutberidze},
journal= {arXiv preprint arXiv:2509.19321},
year = {2025}
}