Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

G. Gát; U. Goginava; G. Tkebuchava

doi:10.1016/j.jmaa.2005.10.056

Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

G. Gát
, U. Goginava
, G. Tkebuchava

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

33 Citations (Scopus)

Abstract

The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L ln L (I²), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category.

Original language	English
Pages (from-to)	535-549
Number of pages	15
Journal	Journal of Mathematical Analysis and Applications
Volume	323
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2005.10.056
Publication status	Published - Nov 1 2006
Externally published	Yes

Keywords

Convergence in measure
Double Walsh-Fourier series
Orlicz space

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jmaa.2005.10.056

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AU - Tkebuchava, G.

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AB - The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Fourier series does not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L ln L (I2), the set of the functions having logarithmic means of quadratical partial sums of the double Walsh-Fourier series convergent in measure is of first Baire category.

KW - Convergence in measure

KW - Double Walsh-Fourier series

KW - Orlicz space

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Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series

Abstract

Keywords

ASJC Scopus subject areas

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