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Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces

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Abstract

We improve and complement a result by Móricz and Siddiqi [20]. In particular, we prove that their estimate of the Nörlund means with respect to the Vilenkin system holds also without their additional condition. Moreover, we prove a similar approximation result in Lebesgue spaces for any \(1\leq p<\infty\).

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Authors and Affiliations

  1. School of Science and Technology, The University of Georgia, 77a Merab Kostava St., Tbilisi 0171, Georgia

    N. Anakidze & L. Baramidze

  2. Faculty of Exact and Natural Sciences, Department of Mathematics, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia

    N. Areshidze

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  1. N. Anakidze
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  2. N. Areshidze
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  3. L. Baramidze
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Correspondence to N. Areshidze.

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The research was supported by Shota Rustaveli National Science Foundation (SRNSF) grant no. MR-23-286.

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Anakidze, N., Areshidze, N. & Baramidze, L. Approximation by Nörlund means with respect to Vilenkin system in Lebesgue spaces. Acta Math. Hungar. (2024). https://doi.org/10.1007/s10474-024-01418-x

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  • DOI: https://doi.org/10.1007/s10474-024-01418-x

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