L1-convergence of fourier series with O-regularly varying quasimonotone coefficients
Journal of Approximation Theory
Journal of Approximation Theory
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In this paper we investigate the trigonometric series with the @b-general monotone coefficients. First, we study the uniform convergence criterion. The estimates of best approximations and moduli of smoothness of the series in uniform metrics are obtained in terms of coefficients. These results imply several important relations between moduli of smoothness of different orders (in particular, Marchaud-type inequality) and best approximations.