On approximating periodic functions using linear approximation methods

In the paper, a generalization of a known theorem by Hardy and Young is obtained; a formula interrelating the integral of a 2π-periodic function over the period with the integral over the entire axis is established; new approximation characteristics for functions belonging to saturation classes of continuity modules of different orders for the spaces L_p of periodic functions are provided, and some issues concerning approximation, in the uniform metric, of continuous periodic functions even with respect to each of their variables and having nonnegative Fourier coefficients are considered. Bibliography: 17 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 337, 2006, pp. 134–164.