Absolute convergence of Vilenkin-Fourier series

DOI10.1016/0022-247X(80)90110-9zbMath0434.43008OpenAlexW2067611461MaRDI QIDQ1139769

Leonard Y. H. Yap, Tong-Seng Quek

Publication date: 1980

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

Full work available at URL: https://doi.org/10.1016/0022-247x(80)90110-9

zbMATH Keywords

absolute convergenceLipschitz functionsVilenkin groups

Mathematics Subject Classification ID

Lipschitz (Hölder) classes (26A16) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Convergence of Fourier series and of inverse transforms (43A50)

Related Items (14)

Absolute convergence of multiple series of Fourier coefficients with respect to multiplicative systems ⋮ Titchmarsh theorems for Fourier transforms of Hölder-Lipschitz functions on compact homogeneous manifolds ⋮ On the Fourier-Walsh transform of functions from dyadic Dini-Lipschitz classes on the semiaxis ⋮ Factorization of Lipschitz functions and absolute convergence of Vilenkin-Fourier series ⋮ Multipliers from one Lipschitz space to another ⋮ Fourier multipliers on compact groups ⋮ Absolute convergence of Fourier series on totally disconnected groups ⋮ Fourier transform of Dini-Lipschitz functions on locally compact Vilenkin groups ⋮ On the absolute convergence of Vilenkin-Fourier series ⋮ Wiener-Ingham type inequality for Vilenkin groups and its application to harmonic analysis ⋮ On the Hankel transform of functions from Nikol'ski type classes ⋮ Fourier transform of Dini-Lipschitz functions on the field of \(p\)-adic numbers ⋮ On the Fourier transform of functions from the classes \(H_p^\alpha ({{\mathbb{R}}})\) ⋮ Fourier transforms of Lipschitz functions and Fourier multipliers on compact groups

Cites Work

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• Absolute convergence of Fourier series on certain groups. II
• Approximation property of functions and absolute convergence of Fourier series
• Uniform convergence of Fourier series on groups. I
• Absolute convergence of Fourier series on certain groups
• On a class of complete orthonormal systems

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