Almost everywhere summability of Fourier series with indication of the set of convergence

DOI10.1134/S0001434616070130zbMath1362.42008arXiv1506.06243MaRDI QIDQ509055

Roald M. Trigub

Publication date: 8 February 2017

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.06243

zbMATH Keywords

Fourier seriesLebesgue pointHardy-Littlewood inequality\(d\)-pointSzidon's inequalityWiener-Banach algebra

Mathematics Subject Classification ID

Trigonometric approximation (42A10) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Related Items (6)

Rogosinsky-Bernstein polynomial method of summation of trigonometric Fourier series ⋮ Summation of Fourier series on the infinite-dimensional torus ⋮ The Fourier transform of bivariate functions that depend only on the maximum of the absolute values of their variables ⋮ Asymptotics of approximation of continuous periodic functions by linear means of their Fourier series ⋮ Wiener algebras and trigonometric series in a coordinated fashion ⋮ Relation between Fourier series and Wiener algebras

Cites Work

• The Wiener algebra of absolutely convergent Fourier integrals: an overview
• A lower bound for the \(L_1\)-norm of a Fourier series of power type.
• Summability of trigonometric Fourier series at $ d$-points and a generalization of the Abel-Poisson method
• On everywhere divergence of trigonometric Fourier series
• Subsequences of the partial sums of a trigonometric series which are everywhere convergent to zero
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