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Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series

Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series The main aim of this paper is to prove that the partial sums of double Vilenkin–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 𝐿ln + 𝐿, the set of functions whose quadratic partial sums of double Vilenkin–Fourier series converge in measure is of first Baire category. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Georgian Mathematical Journal de Gruyter

Convergence in Measure of Partial Sums of Double Vilenkin–Fourier Series

Goginava, Ushangi
Georgian Mathematical Journal , Volume 16 (3) – Sep 1, 2009
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Publisher
de Gruyter
Copyright
© Heldermann Verlag
ISSN
1072-947X
eISSN
1072-9176
DOI
10.1515/GMJ.2009.507
Publisher site
See Article on Publisher Site

Abstract

The main aim of this paper is to prove that the partial sums of double Vilenkin–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 𝐿ln + 𝐿, the set of functions whose quadratic partial sums of double Vilenkin–Fourier series converge in measure is of first Baire category.

Journal

Georgian Mathematical Journal – de Gruyter

Published: Sep 1, 2009

Keywords: Double Vilenkin–Fourier series; Orlicz space; convergence in measure

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