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 for every , where by we denote either the class of continuous functions with supremum norm or the class of integrable functions.
"Norm convergence of logarithmic means on unbounded Vilenkin groups." Banach J. Math. Anal. 12 (2) 422 - 438, April 2018. https://doi.org/10.1215/17358787-2017-0031