On the first derivative of the sums of trigonometric series with quasi-convex coefficients of higher order

Abstract

In this paper, for the sum of sine or cosine series with quasiconvex coefficients of higher order, the representation of their first derivatives are found in terms of the r-th differences of coefficients of the series obtained by formal differentiation. Also some estimates in terms of coefficients of the series are obtained for the integrals of the absolute values of those derivatives.