2021/12/01 by A. S. Belov, Александр Сергеевич Белов, M. I. Dyachenko +3
Mathematics · #Advanced Harmonic Analysis Research #Differential Equations and Boundary Problems #Mathematical Approximation and Integration
paper · doi:10.1070/rm10003
crossref issued 2021/12/01 · crossref published 2021/12/01 · crossref published-print 2021/12/01 · openalex publication_date 2021/12/01 · crossref created 2021/12/27 · crossref deposited 2025/05/12 · openalex created_date 2025/10/10 · crossref indexed 2026/07/28 · openalex updated_date 2026/08/01
Abstract This paper is a study of trigonometric series with general monotone coefficients in the class with . Sharp estimates are proved for the Fourier coefficients of integrable and continuous functions. Also obtained are optimal results in terms of coefficients for various types of convergence of Fourier series. For two-sided estimates are obtained for the -moduli of smoothness of sums of series with -coefficients, as well as for the (quasi-)norms of such sums in Lebesgue, Lorentz, Besov, and Sobolev spaces in terms of Fourier coefficients. Bibliography: 99 titles.