Convergence in Measure of Logarithmic Means of Quadratical Partial Sums of Double Walsh-Kaczmarz-Fourier Series
Keyword(s):
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(I2), 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.
Keyword(s):
2006 ◽
Vol 323
(1)
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pp. 535-549
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2010 ◽
Vol 162
(4)
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pp. 687-708
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2014 ◽
Vol 49
(3)
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pp. 109-116
2014 ◽
Vol 49
(2)
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pp. 70-77