Pointwise approximation by partial sums of Fourier series and conjugate series (Q1111098)

\textit{R. Bojanić} [Publ. Inst. Math. Nouv. Sér. 26(40), 57-60, (1979; Zbl 0451.42004)] has found the estimate of the rate of pointwise convergence of the partial sums of the Fourier series for functions of bounded variation. An estimate af a different nature for the rate of uniforme convergence of these sums corresponding to continuous functions was obtained by \textit{Z. A. Chanturiya} [Mat. Sbornik, N. Ser. 100(142), 534-554 (1976; Zbl 0339.42005)]. The aim of this paper is to obtain the pointwise analogue of Chanturiya's inequality and to extend the Bojanić result to the case of Wiener classes \(BV_ p(p>1)\). Some estimates for the rate of convergence of conjugate sums of the partial sums of the Fourier series are also presented.