Sharp \(H_{p}\)-\(L_{p}\) type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications

DOI10.1186/s13660-016-1182-1zbMath1352.42037OpenAlexW2524106035WikidataQ59460179 ScholiaQ59460179MaRDI QIDQ326435

Lars-Erik Persson, Peter Wall, Lasha Baramidze, Giorgi Tephnadze

Publication date: 12 October 2016

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

Full work available at URL: https://doi.org/10.1186/s13660-016-1182-1

zbMATH Keywords

inequalitiesmaximal operator\(L_p\) spacesVilenkin-Fourier seriesNörlund meansVilenkin systemmartingale Hardy spaceVilenkin group

Mathematics Subject Classification ID

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

Related Items (15)

Some new results and inequalities for subsequences of Nörlund logarithmic means of Walsh-Fourier series ⋮ Approximation by Marcinkiewicz-type matrix transform of Vilenkin-Fourier series ⋮ Convergence of \(T\) means with respect to Vilenkin systems of integrable functions ⋮ 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 ⋮ Approximation by subsequences of matrix transform mean of Walsh-Fourier series ⋮ \((H_p-L_p)\)-type inequalities for subsequences of Nörlund means of Walsh-Fourier series ⋮ Some weak type inequalities and almost everywhere convergence of Vilenkin-Nörlund means ⋮ Martingale Hardy spaces and some new weighted maximal operators of Fejér means of Walsh-Fourier series ⋮ On the rate of approximation by generalized de la Vallée Poussin type matrix transform means of Walsh-Fourier series ⋮ Approximation by matrix transform means with respect to the character system of the group of 2-adic integers ⋮ Unnamed Item ⋮ Approximation by \(\theta\)-means of Walsh-Fourier series in dyadic Hardy spaces and dyadic homogeneous Banach spaces ⋮ Some inequalities related to strong convergence of Riesz logarithmic means ⋮ Approximation by Marcinkiewicz ϴ-means of double Walsh-Fourier series ⋮ Vilenkin-Lebesgue points and almost everywhere convergence for some classical summability methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On the \((C,\alpha)\)-means with respect to the Walsh system
• Approximation by Nörlund means of quadratical partial sums of double Walsh-Fourier series
• \(\theta\)-summability of Fourier series
• On the partial sums of Vilenkin-Fourier series
• Approximation by Nörlund means of Walsh-Fourier series
• Martingale Hardy spaces and their applications in Fourier analysis
• Investigations of certain operators with respect to the Vilenkin system
• Cesàro means of integrable functions with respect to unbounded Vilenkin systems
• \((C,\alpha)\) summability of Walsh-Fourier series
• Strong convergence theorem for Vilenkin-Fourier series
• Strong convergence theorems for Walsh-Fejér means
• Weak inequalities for Cesàro and Riesz summability of Walsh-Fourier series
• Cesàro summability of one- and two-dimensional Walsh-Fourier series
• Strong convergence theorem for Vilenkin--Fejer means
• Approximation by Nӧrlund means of double Walsh-Fourier series for Lipschitz functions
• A note on the maximal operators of Vilenkin—Nörlund means with non-increasing coefficients
• A Maximal Inequality for H 1 -Functions on a Generalized Walsh-Paley Group
• Approximation by Nörlund means of Walsh–Kaczmarz–Fourier series
• On the Nörlund means of Vilenkin-Fourier series
• Norm summability of Nörlund logarithmic means on unbounded Vilenkin groups
• On a generalization of the concept of derivative
• On the maximal operators of Vilenkin-Fejér means on Hardy spaces
• A note on the Fourier coefficients and partial sums of Vilenkin-Fourier series
• On a class of complete orthonormal systems
• Fejér means of Vilenkin-Fourier series
• Cesàro summability with respect to two-parameter Walsh systems
• Strong convergence theorem of Cesàro means with respect to the Walsh system

This page was built for publication: Sharp \(H_{p}\)-\(L_{p}\) type inequalities of weighted maximal operators of Vilenkin-Nörlund means and its applications