The integral modulus of continuity of the Dirichlet kernel and the conjugate Dirichlet kernel

Asymptotic estimates for the integral modulus of continuity of order s of the Dirichlet kernel and the conjugate Dirichlet kernel are obtained. For example, if k/2, then_s(D_k,)=2^s+1/²sin^sk/2 log(1+k/s)+O(2^ssin^sk/2)holds uniformly with respect to all the parameters.Translated from Matematicheskie Zametki, Vol. 54, No. 3, pp. 98–105, September, 1993.