On the Nörlund logarithmic means with respect to Vilenkin system in the martingale Hardy space \(H_1\)

DOI10.1007/s10474-017-0773-8zbMath1399.42082OpenAlexW2771370319MaRDI QIDQ1747958

Lars-Erik Persson, Giorgi Tephnadze, Peter Wall

Publication date: 27 April 2018

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-017-0773-8

zbMATH Keywords

maximal operatorVilenkin-Fourier seriesmartingale Hardy space

Mathematics Subject Classification ID

Maximal functions, Littlewood-Paley theory (42B25) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items (10)

Some new results and inequalities for subsequences of Nörlund logarithmic means of Walsh-Fourier series ⋮ Convergence of \(T\) means with respect to Vilenkin systems of integrable functions ⋮ New fractional maximal operators in the theory of martingale Hardy and Lebesgue spaces with variable exponents ⋮ \((H_p-L_p)\)-type inequalities for subsequences of Nörlund means of Walsh-Fourier series ⋮ An estimate of the maximal operator of the Nörlund logarithmic means with respect to the character system of the group of 2-adic integers on the Hardy space \(H_1\) ⋮ On the \(L^1\) norm of the logarithmic kernel of Walsh-Kaczmarz Fourier series ⋮ Unnamed Item ⋮ Doob’s and Burkholder-Davis-Gundy inequalities with variable exponent ⋮ Maximal operators of T means with respect to Walsh-Kaczmarz system ⋮ Unnamed Item

Cites Work

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• On the partial sums of Vilenkin-Fourier series
• Best approximation by Walsh polynomials
• Approximation by Nörlund means of Walsh-Fourier series
• Martingale Hardy spaces and their applications in Fourier analysis
• The Walsh-Kaczmarz-Marcinkiewicz means and Hardy spaces
• Maximal operators of Vilenkin-Nörlund means
• Strong convergence theorems for Walsh-Fejér means
• On the maximal operators of Walsh-Kaczmarz-Fejér means
• Uniform and \(L\)-convergence of logarithmic means of Walsh-Fourier series
• Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups

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