On approximation of periodic functions by modified Steklov averages in $L_2$

In the space $L_2$ of periodic functions, sharp (in the sence of constants) estimates from below for the deviation of the modified Steklov functions of the first and second order in terms of the modulus of continuity are established. Similar results are also obtained for even continuous periodic functions with nonnegative Fourier coefficients in the space $C$.