Maximal operators of $T$ means with respect to the Vilenkin system
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866911172261838848 |
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| author | Tutberidze, G. |
| author_facet | Tutberidze, G. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_19321 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Maximal operators of $T$ means with respect to the Vilenkin system Tutberidze, G. General Mathematics 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. |
| title | Maximal operators of $T$ means with respect to the Vilenkin system |
| topic | General Mathematics |
| url | https://arxiv.org/abs/2509.19321 |