A note on the strong convergence of partial sums with respect to Vilenkin system

DOI10.3103/S1068362319060062zbMath1440.42139arXiv1802.00341OpenAlexW2998357804MaRDI QIDQ2173212

Yanyan Li

Publication date: 22 April 2020

Published in: Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1802.00341

zbMATH Keywords

strong convergenceHardy spaceVilenkin systempartial sumFejér mean

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Convergence and absolute convergence of Fourier and trigonometric series (42A20)

Related Items (8)

Convergence of \(T\) means with respect to Vilenkin systems of integrable functions ⋮ On the \(L^1\) norm of the logarithmic kernel of Walsh-Kaczmarz Fourier series ⋮ Some problems of convergence of general Fourier series ⋮ Unnamed Item ⋮ Strong convergence theorem for Walsh-Kaczmarz-Fejér means ⋮ A note on the strong summability of two-dimensional Walsh-Fourier series ⋮ Modulus of continuity and convergence of subsequences of Vilenkin-Fejér means in martingale Hardy spaces ⋮ Unnamed Item

Cites Work

• Strong convergence of two-dimensional Walsh-Fourier series
• A note on the norm convergence by Vilenkin-Fejér means
• On the partial sums of Vilenkin-Fourier series
• On the Dirichlet kernels and a Hardy space with respect to the Vilenkin system
• \((L^ 1,H)\)-type estimations for some operators with respect to the Walsh-Paley system
• Martingale Hardy spaces and their applications in Fourier analysis
• Investigations of certain operators with respect to the Vilenkin system
• On an approximation of 2-dimensional Walsh-Fourier series in martingale Hardy spaces
• Strong convergence theorem for Vilenkin-Fourier series
• Maximal operators of Vilenkin-Nörlund means
• A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces
• Strong convergence of two-dimensional Vilenkin-Fourier series
• On the partial sums of Walsh–Fourier series
• A Maximal Inequality for H 1 -Functions on a Generalized Walsh-Paley Group
• Extensions of Hardy spaces and their use in analysis
• TWO-SIDED ESTIMATES OF THE LEBESGUE CONSTANTS WITH RESPECT TO VILENKIN SYSTEMS AND APPLICATIONS
• Summability of Multi-Dimensional Fourier Series and Hardy Spaces
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