Norm convergence of logarithmic means on unbounded Vilenkin groups

György Gát; Ushangi Goginava

doi:10.1215/17358787-2017-0031

Norm convergence of logarithmic means on unbounded Vilenkin groups

György Gát
, Ushangi Goginava

Research output: Contribution to journal › Article › peer-review

11 Citations (Scopus)

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 ∈ X(G), where by X(G) we denote either the class of continuous functions with supremum norm or the class of integrable functions.

Original language	English
Pages (from-to)	422-438
Number of pages	17
Journal	Banach Journal of Mathematical Analysis
Volume	12
Issue number	2
DOIs	https://doi.org/10.1215/17358787-2017-0031
Publication status	Published - Apr 1 2018
Externally published	Yes

Keywords

Convergence in norm
Riesz logarithmic means
Unbounded Vilenkin group

ASJC Scopus subject areas

Analysis
Algebra and Number Theory

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10.1215/17358787-2017-0031

Cite this

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title = "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 ∈ X(G), where by X(G) we denote either the class of continuous functions with supremum norm or the class of integrable functions.",

keywords = "Convergence in norm, Riesz logarithmic means, Unbounded Vilenkin group",

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AU - Gát, György

AU - Goginava, Ushangi

PY - 2018/4/1

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N2 - 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 ∈ X(G), where by X(G) we denote either the class of continuous functions with supremum norm or the class of integrable functions.

AB - 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 ∈ X(G), where by X(G) we denote either the class of continuous functions with supremum norm or the class of integrable functions.

KW - Convergence in norm

KW - Riesz logarithmic means

KW - Unbounded Vilenkin group

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UR - https://www.scopus.com/pages/publications/85044950777#tab=citedBy

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DO - 10.1215/17358787-2017-0031

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EP - 438

JO - Banach Journal of Mathematical Analysis

JF - Banach Journal of Mathematical Analysis

IS - 2

ER -

Norm convergence of logarithmic means on unbounded Vilenkin groups

Abstract

Keywords

ASJC Scopus subject areas

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