Functions with general monotone Fourier coefficients
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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.
functions with general monotone Fourier coefficients, Trigonometric approximation, Convergence and absolute convergence of Fourier and trigonometric series, moduli of smoothness, Besov, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.), Sobolev spaces, Lebesgue, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, estimates of Fourier coefficients, Lorentz
functions with general monotone Fourier coefficients, Trigonometric approximation, Convergence and absolute convergence of Fourier and trigonometric series, moduli of smoothness, Besov, Fourier coefficients, Fourier series of functions with special properties, special Fourier series, Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.), Sobolev spaces, Lebesgue, Sobolev spaces and other spaces of ``smooth'' functions, embedding theorems, trace theorems, estimates of Fourier coefficients, Lorentz
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