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 Algebra i Analiz: Year: Volume: Issue: Page: Find

 Algebra i Analiz, 2013, Volume 25, Issue 4, Pages 125–138 (Mi aa1347)

Research Papers

Almost everywhere convergence of cone-like restricted two-dimensional Fejér means with respect to Vilenkin-like systems

K. Nagy

Institute of Mathematics and Computer Sciences, College of Nyíregyháza, P.O. Box 166, Nyíregyháza, H-4400, Hungary

Abstract: For the two-dimensional Walsh system, Gát and Weisz proved the a.e. convergence of the Fejér means $\sigma_nf$ of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, $\beta^{-1}\leq n_1/n_2\leq\beta$ is ensured with some fixed parameter $\beta\geq1$. The result of Gát and Weisz was generalized by Gát and the author in the way that the indices are inside a cone-like set.
In the present paper, the a.e. convergence is proved for the Fejér means of integrable functions with respect to two-dimensional Vilenkin-like systems provided that the set of indeces is in a cone-like set. That is, the result of Gát and the author is generalized to a general orthonormal system, which contains as special cases the Walsh system, the Vilenkin system, the character system of the group of 2-adic integers, the UDMD system, and the representative product system of CTD (compact totally disconnected) groups.

Keywords: Vilenkin group, Vilenkin system, pointwise convergence, Fejér means, orthonormal systems, two-dimensional Fourier series, compact totally disconnected group.

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English version:
St. Petersburg Mathematical Journal, 2014, 25:4, 605–614

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Citation: K. Nagy, “Almost everywhere convergence of cone-like restricted two-dimensional Fejér means with respect to Vilenkin-like systems”, Algebra i Analiz, 25:4 (2013), 125–138; St. Petersburg Math. J., 25:4 (2014), 605–614

Citation in format AMSBIB
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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. K. Nagy, “On the restricted summability of two-dimensional Walsh-Fejér means”, Publ. Math. Debrecen, 85:1-2 (2014), 113–122
2. I. Blahota, K. Nagy, “On the restricted summability of the multi-dimensional Vilenkin–Cesaro means”, J. Math. Inequal., 11:4 (2017), 997–1006
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