Abstract
A theorem of Lukacs [J. Reine Angew. Math., 150, 107–112 (1920)] states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function f diverge with a logarithmic rate at the points of discontinuity of f of the first kind. Moricz [Acta Math. Hung., 98, 259–262 (2003)] proved a similar theorem for the rectangular partial sums of double conjugate trigonometric Fourier series. We consider analogs of the Moricz theorem for the generalized Cesaro means and positive linear means. In the present paper we prove a similar theorem in terms of linear operators satisfying certain conditions.
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