Abstract:
For the Dirichlet classes $\mathscr D_p$ of holomorphic functions in the disk, we obtain the exact orders of best polynomial approximations and of upper bounds for deviations of Fejér means of Taylor series in the Hardy spaces $H_p$.
Keywords:Dirichlet class of holomorphic functions, Fejér mean, best polynomial approximation, Taylor series, Hardy space, Fubini theorem, Riesz theorem.