On summability of Fourier coefficients of functions from Lebesgue space

DOI10.1016/j.jmaa.2014.05.024zbMath1298.42007OpenAlexW2075614115MaRDI QIDQ2252310

M. I. D'yachenko, E. D. Nursultanov, Ayagoz Kankenova

Publication date: 17 July 2014

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

Full work available at URL: https://doi.org/10.1016/j.jmaa.2014.05.024

zbMATH Keywords

Fourier seriesFourier coefficientsHardy-Littlewood theorem

Mathematics Subject Classification ID

Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) (42A32)

Related Items (7)

Normal periodic solutions for the fractional abstract Cauchy problem ⋮ Weighted Fourier inequalities and boundedness of variation ⋮ Functions with general monotone Fourier coefficients ⋮ Hardy-type theorems on Fourier transforms revised ⋮ Hardy-Littlewood and Pitt's inequalities for Hausdorff operators ⋮ Asymptotics of sums of sine series with fractional monotonicity coefficients ⋮ Smoothness of functions and Fourier coefficients

Cites Work

• Net spaces and boundedness of integral operators
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• Trigonometric series with general monotone coefficients
• Trigonometric series of Nikol'skii classes
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• Interpolation of Besov \(B^{\sigma q}_{p\tau}\) and Lizorkin-Triebel \(F^{\sigma q}_{p\tau}\) spaces
• A Hardy-Littlewood theorem for multiple series
• Integrability and continuity of functions represented by trigonometric series: coefficients criteria
• ON THE CONVERGENCE OF DOUBLE TRIGONOMETRIC SERIES AND FOURIER SERIES WITH MONOTONE COEFFICIENTS
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