Strong convergence theorem for Vilenkin-Fourier series

DOI10.1006/jmaa.2000.6732zbMath0987.42022OpenAlexW2068623811MaRDI QIDQ1977775

Peter L. Simon

Publication date: 18 June 2002

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.2000.6732

zbMATH Keywords

atomic decompositionHardy spacesVilenkin-Fourier series

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10)

Related Items (20)

Some new results and inequalities for subsequences of Nörlund logarithmic means of Walsh-Fourier series ⋮ Sharp \(H_{p}\)-\(L_{p}\) type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications ⋮ On the Nörlund means of Vilenkin-Fourier series ⋮ Sharp $(H_p,L_p)$ and $(H_p,\text{weak}-L_p)$ type inequalities of weighted maximal operators of $T$ means with respect to Vilenkin systems ⋮ A note on the strong convergence of partial sums with respect to Vilenkin system ⋮ Strong convergence of two-dimensional Walsh-Fourier series ⋮ \((H_p-L_p)\)-type inequalities for subsequences of Nörlund means of Walsh-Fourier series ⋮ Almost everywhere convergence of \(T\) means with respect to the Vilenkin system of integrable functions ⋮ Strong convergence theorems for Walsh-Fejér means ⋮ Unnamed Item ⋮ On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces ⋮ Strong convergence theorem for Walsh-Kaczmarz-Fejér means ⋮ On the \((C,\alpha)\)-means with respect to the Walsh system ⋮ Strong convergence of two-dimensional Vilenkin-Fourier series ⋮ Strong convergence theorem of Cesàro means with respect to the Walsh system ⋮ On the partial sums of Vilenkin-Fourier series ⋮ A note on the strong summability of two-dimensional Walsh-Fourier series ⋮ Some new results on the strong convergence of Fejér means with respect to Vilenkin systems ⋮ Fourier multiplier theorem for atomic Hardy spaces on unbounded Vilenkin groups ⋮ Sharp \((H_p, L_p)\) type inequalities of maximal operators of \(T\) means with respect to Vilenkin systems

Cites Work

• Strong convergence of certain means with respect to the Walsh-Fourier series
• Hardy-Littlewood type inequalities for Vilenkin-Fourier coefficients
• Martingale Hardy spaces and their applications in Fourier analysis
• Investigations of certain operators with respect to the Vilenkin system
• Strong convergence theorems for two-parameter Walsh-Fourier and trigonometric-Fourier series
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