On approximating periodic functions by singular integrals with positive kernels

In the two-dimensional case, new approximation characteristics for functions belonging to saturation classes of continuity modules for the spaces L_p of periodic functions are obtained. The problem of approximating a function by an analog of Fejér’s integral in the space of periodic functions square integrable on the period is considered. Bibliography: 5 titles. Dedicated to the 100th anniversary of G. M. Goluzin’s birthday __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 51–72.