Georgian Mathematical Journal 13 (2006), No. 3, 447--462
Copyright Heldermann Verlag 2006
Almost Everywhere Convergence of (C, α)-Means of Quadratical Partial Sums of Double Vilenkin-Fourier Series
György Gát
Inst. of Mathematics and Computer Science, College of Nyíregyháza, P. O. Box 166, Nyíregyháza 4400, Hungary
gatgy@zeus.nyf.hu
Ushangi Goginava
Inst. Mechanics and Mathematics, Faculty of Exact and Natural Sciences, I. Javakhishvili University, 1 Chavchavadze Ave., Tbilisi 0128, Georgia
z_goginava@hotmail.com
[Abstract-pdf]
We prove that the maximal operator of the $\(C,\alpha\)$-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). Moreover, the $(C,\alpha)$-means $t_{n}^{\alpha}f$ of a function $f\in L^{1}$ converge a.e. to $f$ as $n\rightarrow \infty$.
Keywords: Cesaro means, Vilenkin system, almost everywhere convergence.
MSC: 42C10
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