Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series. (4th January 2012)

• Record Type: Journal Article
• Authors: Goginava, Ushangi; Nagy, Károly
• Other Names: Kaminska Anna Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-01-04
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/582726
• Languages: English
• ISSNs: 0972-6802

Abstract

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 ofL 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.