Abstract:
We consider functions represented as trigonometric series with general monotone Fourier coefficients. The main result of the paper is the equivalence of the $L_p$ modulus of smoothness, $1<p<\infty$, of such functions to certain sums of their Fourier coefficients. As applications, for such functions we give a description of the norm in the Besov space and sharp direct and inverse theorems in approximation theory.
Bibliography: 34 titles.
Keywords:Fourier series, general monotone sequences, moduli of smoothness.
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