On the Lebesgue test for convergence of Fourier series on unbounded Vilenkin groups

DOI10.1007/S10474-010-0023-9zbMath1274.43006OpenAlexW2036440027WikidataQ57621865 ScholiaQ57621865MaRDI QIDQ626050

Nacima Memić, Muharem Avdispahić

Publication date: 25 February 2011

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-010-0023-9

zbMATH Keywords

Fourier seriesVilenkin groupLebesgue test

Mathematics Subject Classification ID

Harmonic analysis on specific compact groups (43A75) Convergence of Fourier series and of inverse transforms (43A50)

Related Items (6)

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 ⋮ On the convergence of partial sums with respect to Vilenkin system on the martingale Hardy spaces ⋮ Norm convergence of double Fourier series on unbounded Vilenkin groups ⋮ Norm convergence of logarithmic means on unbounded Vilenkin groups ⋮ A sharp boundedness result for restricted maximal operators of Vilenkin-Fourier series on martingale Hardy spaces

Cites Work

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• Fourier multiplier theorem for atomic Hardy spaces on unbounded Vilenkin groups
• On the divergence of Vilenkin-Fourier series
• On \(L^p\)-norm convergence of series with respect to product systems
• An integrability theorem on unbounded Vilenkin groups
• Cesàro means of integrable functions with respect to unbounded Vilenkin systems
• On the Lebesgue test for the convergence of Vilenkin-Fourier series
• Pointwise convergence of the Fejér means of functions on unbounded Vilenkin groups
• Uniform convergence of Fourier series on groups. I
• Fourier Analysis on Local Fields. (MN-15)
• Mean Convergence of Generalized Walsh-Fourier Series
• Verallgemeinerte Walsh—Fourierreihen. II

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