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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(ω) 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.

Pointwise approximation of modified conjugate functions by matrix operators of their Fourier series