Norm convergence of logarithmic means on unbounded Vilenkin groups

Abstract

In this paper we prove that, in the case of some unbounded Vilenkin groups, the Riesz logarithmic means converges in the norm of the spaces $X\left(G\right)$ for every $f\in X\left(G\right)$, where by $X\left(G\right)$ we denote either the class of continuous functions with supremum norm or the class of integrable functions.