On the Rate of Pointwise Strong Summability of Fourier Series

Abstract

Abstract. There is introduced a modified local modulus of continuity as a measure of pointwise strong summability. The approximation versions of known results PuTraing Wang [6] and A. A. Zakhaxov [8] are obtained. IntroductionLet LP (1 < p < oo) [resp.C] be the class of all 27r-periodic real-valued functions integrable in the Lebesgue sense with p-th power [continuous] over Q = [-7T, 7r]

Approximation of integrable functions by general linear operators of their fourier series

“…We note that in the case A = 1 n+1 the conditions of the above theorems are fulfilled and the relation (2.10) leads us to the result comparable with [3] on approximation of f by the Cesàro means (C, 2) of its Fourier series.…”