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

Access to Document

10.1007/s10114-005-0648-8

Cite this

@article{8c1bba7a80904dbbb2f22c42fad10621,

title = "Uniform and L-convergence of logarithmic means of Walsh-Fourier series",

abstract = "The (N{\"o}rlund) 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.",

keywords = "Convergence divergence properties, N{\"o}rlund logarithmic means, Walsh system",

author = "G. G{\'a}t and U. Goginava",

year = "2006",

month = apr,

doi = "10.1007/s10114-005-0648-8",

language = "English",

volume = "22",

pages = "497--506",

journal = "Acta Mathematica Sinica, English Series",

issn = "1439-8516",

publisher = "Springer Verlag",

number = "2",

}

TY - JOUR

T1 - Uniform and L-convergence of logarithmic means of Walsh-Fourier series

AU - Gát, G.

AU - Goginava, U.

PY - 2006/4

Y1 - 2006/4

N2 - 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.

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

UR - https://www.scopus.com/pages/publications/33644928997

UR - https://www.scopus.com/inward/citedby.url?scp=33644928997&partnerID=8YFLogxK

U2 - 10.1007/s10114-005-0648-8

DO - 10.1007/s10114-005-0648-8

M3 - Article

AN - SCOPUS:33644928997

SN - 1439-8516

VL - 22

SP - 497

EP - 506

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 2

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this