DETERMINATION OF JUMPS IN TERMS OF LINEAR OPERATORS

Author: Shalva Zviadadze
Keywords: Trigonometric series, Linear means
Annotation:

A theorem of Ferenc Lukacs states that the partial sums conjugate Fourier series of periodic Lebesgue integrable function diverge by logarithmic rate at the points of discontinuity. Moricz proved analogous theorem for the rectangular partial sums of double variable functions. We consider analogues of Moricz theorem for generalized Cesaro means and for positive linear means. In the present talk we consider analogue theorem in terms of linear operators which satisfy some certain conditions.