Growth of norms in $L_2$ of derivatives of Steklov functions and properties of functions defined by best approximations and Fourier coefficients

In the paper, for periodic functions, a connection between integrals of norms in $L_2$ of derivatives of Steklov functions and series constructed from Fourier coefficients and the best approximations in $L_2$ is established, and the question on their simultaneous convergence or divergence is considered. Similar investigations are carried out for even and odd periodic functions.