## Banach Journal of Mathematical Analysis

### 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 $X(G)$ for every $f\in X(G)$, where by $X(G)$ we denote either the class of continuous functions with supremum norm or the class of integrable functions.

#### Article information

Source
Banach J. Math. Anal., Volume 12, Number 2 (2018), 422-438.

Dates
Accepted: 17 July 2017
First available in Project Euclid: 17 November 2017

https://projecteuclid.org/euclid.bjma/1510909224

Digital Object Identifier
doi:10.1215/17358787-2017-0031

Mathematical Reviews number (MathSciNet)
MR3779721

Zentralblatt MATH identifier
06873508

#### Citation

Gát, György; Goginava, Ushangi. Norm convergence of logarithmic means on unbounded Vilenkin groups. Banach J. Math. Anal. 12 (2018), no. 2, 422--438. doi:10.1215/17358787-2017-0031. https://projecteuclid.org/euclid.bjma/1510909224

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