On Convergence and Divergence of Fourier Series and Féjer Means with Applications to Lebesgue and Vilenkin-Lebesgue Points

Nadirashvili, Nato; Nasibov, Tural

doi:10.1007/978-3-031-62894-8_16

Trends in Mathematics

2024

DOI: 10.1007/978-3-031-62894-8_16

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On Convergence and Divergence of Fourier Series and Féjer Means with Applications to Lebesgue and Vilenkin-Lebesgue Points

Nato Nadirashvili,

Tural Nasibov

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2024

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Cited by 1 publication

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

Areshidze,

Persson,

Tephnadze

2024

Mediterr. J. Math.

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We characterize subsequences $$\{S_{n_k}\}$$ { S n k } of partial sums with respect to (bounded or unbounded) Vilenkin systems of $$f\in L^1(G_m)$$ f ∈ L 1 ( G m ) for which almost everywhere convergence holds. Moreover, we construct an explicit $$f\in L^p(G_m), \ 1\le p<\infty $$ f ∈ L p ( G m ) , 1 ≤ p < ∞ 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–Féjer means.

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

Areshidze,

Persson,

Tephnadze

2024

Mediterr. J. Math.

View full text Add to dashboard Cite

show abstract

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On Convergence and Divergence of Fourier Series and Féjer Means with Applications to Lebesgue and Vilenkin-Lebesgue Points

Cited by 1 publication

References 33 publications

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

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

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