Almost everywhere convergence of $T$ means  with respect to the Vilenkin system of integrable functions

N.  Nadirashvili

doi:10.37863/umzh.v75i7.7163

N. Nadirashvili University of Georgia, School of Science and Technology, Tbilisi

DOI: https://doi.org/10.37863/umzh.v75i7.7163

Keywords: Vilenkin groups, Vilenkin systems, partial sums of Vilenkin-Fourier series, $T$ means, Fejér mean, Riesz means, $L_{p}$ spaces, $weak-L_{p}$ spaces, maximal operator, inequalities.

Abstract

UDC 517.5

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 monotone coefficients. We also apply these 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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