An analogy of the Carleson-Hunt theorem with respect to Vilenkin systems
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Publication:2146298
DOI10.1007/s00041-022-09938-2zbMath1492.42032OpenAlexW4280552574WikidataQ113906222 ScholiaQ113906222MaRDI QIDQ2146298
Lars-Erik Persson, Ferenc Weisz, Ferenc Schipp, Giorgi Tephnadze
Publication date: 16 June 2022
Published in: The Journal of Fourier Analysis and Applications (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00041-022-09938-2
Fourier analysisVilenkin-Fourier seriesVilenkin systemalmost everywhere convergenceVilenkin groupCarleson-Hunt theoremKolmogorov theorem
Maximal functions, Littlewood-Paley theory (42B25) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Summability and absolute summability of Fourier and trigonometric series (42A24)
Related Items (12)
Some new results and inequalities for subsequences of Nörlund logarithmic 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 ⋮ Some new weak (\(H_p\)-\(L_p\))-type inequality for weighted maximal operators of partial sums of Walsh-Fourier series ⋮ Some new \((H_p -L_p)\) type inequalities for weighted maximal operators of partial sums 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 ⋮ Products and commutators of martingales in \(H_1\) and BMO ⋮ Almost everywhere convergence of \(T\) means with respect to the Vilenkin system of integrable functions ⋮ Some problems of convergence of general Fourier series ⋮ Unnamed Item ⋮ Vilenkin-Lebesgue points and almost everywhere convergence for some classical summability methods
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