On some properties of conjugate trigonometric Fourier series

A theorem of Ferenc Lukacs states that the partial sums of conjugate Fourier series of a periodic Lebesgue integrable function f diverge at the logarithmic rate at the points of first kind discontinuity of f. The aim of this paper is to prove analogous theorems in terms of generalized Cesar means, introduced by Akhobadze, as well as regular linear means. We also formulate analogous theorems in terms of Abel Poisson means for functions and series introduced by Taberslci.