We extend the results presented by Xh. Z. Krasniqi (Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of Lp. Acta Comment. Univ. Tartu. Math., 2013, 17, 89–101) and W. Lenski and B. Szal (Approximation of functions belonging to the class Lp(w) by linear operators. Acta Comment. Univ. Tartu. Math., 2009, 13, 11–24) to the case when a conjugate function depends on r and where in the measures of estimations r-differences of the entries are used.
1. Krasniqi, Xh. Z. Slight extensions of some theorems on the rate of pointwise approximation of functions from some subclasses of Lp. Acta Comment. Univ. Tartu. Math., 2013, 17, 89–101.
2. Lenski, W. and Szal, B. Approximation of functions belonging to the class Lp(w) by linear operators. Acta Comment. Univ. Tartu. Math., 2009, 13, 11–24.
3. Szal, B. A new class of numerical sequences and its applications to uniform convergence of sine series. Math. Nachr., 2011, 284, 1985–2002.
https://doi.org/10.1002/mana.200910061
4. Szal, B. On L-convergence of trigonometric series. J. Math. Anal. Appl., 2011, 373, 449–463.
5. Zygmund, A. Trigonometric Series. Cambridge University Press, 2002.
https://doi.org/10.1016/j.jmaa.2010.08.003
