On some properties of double conjugate trigonometric Fourier series

Abstract

A theorem of Ferenc Lukacs [4] states that the partial sums of conjugate Fourier series of periodic Lebesgue integrable functions f diverge at logarithmic rate at the points of discontinuity of first kind of f. F. Moricz [5] proved an analogous theorem for the rectangular partial sums of bivariate functions. The present paper proves analogues of Moricz’s theorem for generalized Cesaro means and for positive linear means.