Order estimates of smallest norms, with respect to the choice of $N$ harmonics, of derivatives of the Dirichlet and Favard kernels

The Dirichlet kernel is defined for periodic functions of several variables; it consists of $N$ harmonics and has minimal order of the norm with respect to the choice of harmonics of the mixed Weyl derivative in the space $\tilde L_q$. A similar problem on the minimal order of the norm is solved for the Favard kernel. Both problems generalize to the case of several derivatives.