Approximation by $T$ means with respect to Vilenkin system in Lebesgue spaces

N. Anakidze^a, N. Areshidze^b, L.-E. Persson^cd, G. Tephnadze<sup>a

a</sup> School of Science and Technology, The University of Georgia, 77a Merab Kostava St, 0171 Tbilisi, Georgia
^b Department of Mathematics, University of California, Irvine, 480 Rowland Hall, 92697 Irvine, CA, USA
^c Department of Mathematics, Uppsala University, Uppsala, Sweden
^d Department of Mathematics and Computer Science, UiT The Arctic University of Norway, Sweden

Abstract: In this paper we present and prove some new results concerning approximation properties of $T$ means with respect to the Vilenkin system in Lebesgue spaces for any $1\leqslant p<\infty$. As applications, we obtain extensions of some known approximation inequalities.

Keywords and phrases: Vilenkin group, Vilenkin system, $T$ means, Nörlund means, Fejér means, approximation, Lebesgue spaces, inequalities.

MSC: 42C10

Received: 18.10.2024

Language: English

DOI: 10.32523/2077-9879-2025-16-4-08-22