Convergence in measure of logarithmic means of quadratical partial sums of double Walsh-Fourier series |
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| Authors: | G. Gá t,U. Goginava |
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| Affiliation: | a Institute of Mathematics and Computer Science, College of Nyíregyháza, PO Box 166, Nyíregyháza, H-4400 Hungary
b Department of Mechanics and Mathematics, Tbilisi State University, Chavchavadze str. 1, Tbilisi 0128, Georgia |
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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-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 LlnL(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. |
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| Keywords: | Double Walsh-Fourier series Orlicz space Convergence in measure |
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