Approximation of holomorphic functions by Taylor-Abel-Poisson means

Abstract

We investigate approximations of functions $f$ holomorphic in the unit disk by means $A_{\rho, r}(f)$ for $\rho \rightarrow 1_-$. In terms of an error of the approximation by these means, the constructive characteristic of classes of holomorphic functions $H_p^r \text{\;Lip\,}\alpha$ is given. The problem of the saturation of $A_{\rho, r}(f)$ in the Hardy space $H_p$ is solved.