Convergence in measure of logarithmic means of double walsh-fourier series

GYÖORGY GÁT; Ushangi Goginava; George Tkebuchava

doi:10.1515/GMJ.2005.607

Convergence in measure of logarithmic means of double walsh-fourier series

GYÖORGY GÁT
, Ushangi Goginava
, George Tkebuchava

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

10 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log L(I²), the set of functions for which quadratic logarithmic means of the doubleWalsh-Fourier series converge in measure is of first Baire category.

Original language	English
Pages (from-to)	607-618
Number of pages	12
Journal	Georgian Mathematical Journal
Volume	12
Issue number	4
DOIs	https://doi.org/10.1515/GMJ.2005.607
Publication status	Published - 2005
Externally published	Yes

Keywords

convergence in measure
Double Walsh-Fourier series
Orlicz space

ASJC Scopus subject areas

General Mathematics

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10.1515/GMJ.2005.607

Cite this

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abstract = "The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log L(I2), the set of functions for which quadratic logarithmic means of the doubleWalsh-Fourier series converge in measure is of first Baire category.",

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AU - Tkebuchava, George

PY - 2005

Y1 - 2005

N2 - The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log L(I2), the set of functions for which quadratic logarithmic means of the doubleWalsh-Fourier series converge in measure is of first Baire category.

AB - The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log L(I2), the set of functions for which quadratic logarithmic means of the doubleWalsh-Fourier series converge in measure is of first Baire category.

KW - convergence in measure

KW - Double Walsh-Fourier series

KW - Orlicz space

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UR - https://www.scopus.com/pages/publications/71449095705#tab=citedBy

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M3 - Article

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JO - Georgian Mathematical Journal

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ER -

Convergence in measure of logarithmic means of double walsh-fourier series

Abstract

Keywords

ASJC Scopus subject areas

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