Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin

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Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series

Published:2006-09 Issue:3 Volume:13 Page:447-462
ISSN:1572-9176
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language:en
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Author:

Gát György¹,Goginava Ushangi²

Affiliation:

1. Institute of Mathematics and Computer Science, College of Nyíregyháza, P.O. Box 166, Nyiregyháza, H-4400, Hungary. E-mail:

2. Institute of Mechanics and Mathematics, Faculty of Exact and Natural Sciences, I. Javakhishvili Tbilisi State University, 1, Chavchavadze Ave., Tbilisi 0128, Georgia. E-mail:

Abstract

Abstract We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Cited by 3 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Matrix transformations of sequences and applications in Fourier analysis;Heliyon;2024-04

2. Almost Everywhere Convergence of Cesàro-Marczinkiewicz Means of Two-Dimensional Fourier Series on the Group of $$2$$-Adic Integers;p-Adic Numbers, Ultrametric Analysis and Applications;2022-05-23

3. On the L 1 Norm of the Weighted Maximal Function of Walsh-Marcinkiewicz Kernels;Inequalities and Applications 2010;2012

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