Approximation of holomorphic functions by Cesàro means

• Date: 2022
• Main Authors: Rovenska , O. G., Savchuk , V. V., Savchuk, M. V., Ровенська, О. Г., Савчук, В. В., Савчук , М. В., Савчук, Віктор Васильович
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2022
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/7143
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

UDC 517.5 For the Lipschitz class of functions holomorphic in the disc, we present a constructive characterization of this class in terms of Cesaro’s means of order $\alpha \ge 2$ of the Taylor series. We solve the problem of exact upper bound for the deviations of Cesaro’s means of order $\alpha \g...