Convergence Almost Everywhere of Partial Sums and Féjer Means of Vilenkin-Fourier Series

被引：1

作者：

Areshidze, N. ^{[1
]}

Persson, L. -e. ^{[2
,3
]}

Tephnadze, G. ^{[4
]}

机构：

[1] Univ Calif Irvine, Dept Math, Irvine, CA 92617 USA

[2] UiT Arctic Univ Norway, POB 385, N-8505 Narvik, Norway

[3] Uppsala Univ, Dept Math, POB 480 751 06, S-75238 Uppsala, Sweden

[4] Univ Georgia, Sch Sci & Technol, 77a Merab Kostava St, Tbilisi 0171, Georgia

来源：

MEDITERRANEAN JOURNAL OF MATHEMATICS | 2025年 / 22卷 / 01期

关键词：

Fourier analysis; Vilenkin-Fourier series; Subsequences; Almost everywhere convergence; F & eacute; jer means; Divergence on a set of measure zero; FEJER MEANS; DIVERGENCE; SETS; RESPECT; SUMMABILITY; SYSTEMS;

D O I：

10.1007/s00009-024-02783-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We characterize subsequences {S-nk} of partial sums with respect to (bounded or unbounded) Vilenkin systems of f is an element of L-1(Gm) for which almost everywhere convergence holds. Moreover, we construct an explicit f is an element of L-p(G(m)), 1 <= p < infinity whose partial sums (satisfying the same conditions which guarantee almost everywhere convergence) diverges on any set of measure zero. We also prove a similar divergence result for Vilenkin-Fejer means.

引用

页数：17

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