Convergence in Measure of Logarithmic Means of Double Walsh–Fourier Series-Reference-Cited by-同舟云学术

Convergence in Measure of Logarithmic Means of Double Walsh–Fourier Series

Published:2005-12 Issue:4 Volume:12 Page:607-618
ISSN:1572-9176
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language:en
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Author:

Gát György¹,Goginava Ushangi²,Tkebuchava George²

Affiliation:

1. Institute of Mathematics and Computer Science, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400 Hungary. E-mail:

2. Department of Mechanics and Mathematics, I. Javakhishvili Tbilisi State University, 1, Chavchavadze Ave., Tbilisi 0128, Georgia. E-mail:

Abstract

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 𝐿log 𝐿(𝐼2), the set of functions for which quadratic logarithmic means of the double Walsh–Fourier series converge in measure is of first Baire category.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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