Multiplicative convolutions of functions from Lorentz spaces and convergence of series of Fourier-Vilenkin coefficients

DOI10.3103/S1066369X17050048zbMath1377.42005MaRDI QIDQ2399449

Maria A. Kuznetsova, Sergey S. Volosivets

Publication date: 23 August 2017

Published in: Russian Mathematics (Search for Journal in Brave)

zbMATH Keywords

Lorentz spacebest approximationFourier coefficientsmultiplicative systemmultiplicative convolution

Mathematics Subject Classification ID

Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Best approximation, Chebyshev systems (41A50) Convergence and absolute convergence of Fourier and trigonometric series (42A20) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16)

Cites Work

• On certain conditions in the theory of series with respect to multiplicative systems
• On the best approximation of functions with respect to multiplicative systems and the properties of their Fourier coefficients
• Convergence of series of Fourier coefficients for multiplicative convolutions
• On absolutely convergent Fourier series
• Absolute convergence of Fourier series on certain groups. II
• Convolution functions on compact Abelian groups
• On Hardy and Bellman transforms of series with respect to multiplicative systems in symmetric spaces
• Convolution operators and L(p, q) spaces
• Absolute convergence of Fourier series of convolution functions
• On L(p,q) spaces
• Mean Convergence of Generalized Walsh-Fourier Series
• Subsequences of the partial sums of a trigonometric series which are everywhere convergent to zero
• An application of interpolation theory to Fourier series
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