Banach Journal of Mathematical Analysis

Norm convergence of logarithmic means on unbounded Vilenkin groups

György Gát and Ushangi Goginava

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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 fX(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
Received: 28 March 2017
Accepted: 17 July 2017
First available in Project Euclid: 17 November 2017

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1510909224

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

Mathematical Reviews number (MathSciNet)
MR3779721

Zentralblatt MATH identifier
06873508

Subjects
Primary: 42C10: Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.)
Secondary: 40G99: None of the above, but in this section

Keywords
unbounded Vilenkin group Riesz logarithmic means convergence in norm

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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