2017
Том 69
№ 9

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Approximation of holomorphic functions by Taylor-Abel-Poisson means

Savchuk V. V.

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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.

English version (Springer): Ukrainian Mathematical Journal 59 (2007), no. 9, pp 1397-1407.

Citation Example: Savchuk V. V. Approximation of holomorphic functions by Taylor-Abel-Poisson means // Ukr. Mat. Zh. - 2007. - 59, № 9. - pp. 1253–1260.

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