Uniform and L-convergence of logarithmic means of Walsh-Fourier series

G. Gát; U. Goginava

doi:10.1007/s10114-005-0648-8

Uniform and L-convergence of logarithmic means of Walsh-Fourier series

G. Gát, U. Goginava

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

42 Citations (Scopus)

Abstract

The (Nörlund) logarithmic means of the Fourier series of the integrable function f is: 1/ln Σ_k=1^n-1 Sk (f)/n -k, where ln:= Σ_k=1^n-1 1/k. In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L¹ Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Moricz concerning the convergence of logarithmic means in norm.

Original language	English
Pages (from-to)	497-506
Number of pages	10
Journal	Acta Mathematica Sinica, English Series
Volume	22
Issue number	2
DOIs	https://doi.org/10.1007/s10114-005-0648-8
Publication status	Published - Apr 2006
Externally published	Yes

Keywords

Convergence divergence properties
Nörlund logarithmic means
Walsh system

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s10114-005-0648-8

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AU - Goginava, U.

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AB - The (Nörlund) logarithmic means of the Fourier series of the integrable function f is: 1/ln Σk=1n-1 Sk (f)/n -k, where ln:= Σk=1n-1 1/k. In this paper we discuss some convergence and divergence properties of this logarithmic means of the Walsh-Fourier series of functions in the uniform, and in the L1 Lebesgue norm. Among others, as an application of our divergence results we give a negative answer to a question of Moricz concerning the convergence of logarithmic means in norm.

KW - Convergence divergence properties

KW - Nörlund logarithmic means

KW - Walsh system

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Uniform and L-convergence of logarithmic means of Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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