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Almost Everywhere Convergence of T Means with Respect to the Vilenkin System of Integrable Functions

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Ukrainian Mathematical Journal Aims and scope

We prove and discuss some new weak-type (1,1) inequalities for the maximal operators of T means with respect to the Vilenkin system generated by monotonic coefficients. We also apply the accumulated results to prove that these T means are almost everywhere convergent. As applications, we present both some well-known and new results.

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Authors and Affiliations

  1. School of Science and Technology, University of Georgia, Tbilisi, Georgia

    N. Nadirashvili

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Correspondence to N. Nadirashvili.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 7, pp. 933–945, July, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i7.7163.

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Nadirashvili, N. Almost Everywhere Convergence of T Means with Respect to the Vilenkin System of Integrable Functions. Ukr Math J 75, 1067–1080 (2023). https://doi.org/10.1007/s11253-023-02247-x

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  • DOI: https://doi.org/10.1007/s11253-023-02247-x

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