The weak type inequality for the maximal operator of the Marcinkiewicz-Fejér means of the two-dimensional Walsh-Fourier series

DOI10.1016/j.jat.2008.03.012zbMath1183.42028OpenAlexW2060310284MaRDI QIDQ999272

Ushangi Goginava

Publication date: 3 February 2009

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2008.03.012

zbMATH Keywords

Hardy spaceWalsh functionMarcinkiewicz-Fejér means

Mathematics Subject Classification ID

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

Related Items (13)

The martingale Hardy type inequality for Marcinkiewicz-Fejér means of two-dimensional conjugate Walsh-Fourier series ⋮ Strong convergence of two-dimensional Walsh-Fourier series ⋮ Almost everywhere strong summability of double Walsh-Fourier series ⋮ Weak type inequalities for the \(\ell_1\)-summability of higher dimensional Fourier transforms ⋮ Convergence in measure of strong logarithmic means of double Fourier series ⋮ BMO-estimation and almost everywhere exponential summability of quadratic partial sums of double Fourier series ⋮ Triangular Fejér summability of two-dimensional Walsh-Fourier series ⋮ Walsh-Marcinkiewicz means and Hardy spaces ⋮ Approximation by Walsh-Marcinkiewicz means on the Hardy space \(H_{2/3}\) ⋮ Sharp weak type inequalities for fractional integral operators ⋮ Strong convergence of two-dimensional Vilenkin-Fourier series ⋮ Sharp weak type inequality for fractional integral operators associated with \(d\)-dimensional Walsh-Fourier series ⋮ On the maximal operators of weighted Marcinkiewicz type means of two-dimensional Walsh-Fourier series

Cites Work

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• Marcinkiewicz-Fejér means of \(d\)-dimensional Walsh--Fourier series
• \(\theta\)-summability of Fourier series
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• A Maximal Inequality for H 1 -Functions on a Generalized Walsh-Paley Group
• On (C,1) summability of integrable functions with respect to the Walsh-Kaczmarz system
• CESARO SUMMABILITY OF WALSH-FOURIER SERIES
• Cesàro summability with respect to two-parameter Walsh systems

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