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

Ushangi Goginava; Károly Nagy

doi:10.1155/2012/582726

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

Ushangi Goginava, Károly Nagy

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

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Abstract

The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz 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 log ⁺ L(I ²), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category.

Original language	English
Article number	582726
Journal	Journal of Function Spaces and Applications
DOIs	https://doi.org/10.1155/2012/582726
Publication status	Published - 2012
Externally published	Yes

ASJC Scopus subject areas

Analysis

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abstract = "The main aim of this paper is to prove that the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz 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 log + L(I 2), the set of the functions the logarithmic means of quadratical partial sums of the double Walsh-Kaczmarz series of which converge in measure is of first Baire category.",

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

Abstract

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