Approximation of holomorphic functions by Cesàro means
Abstract
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 $\alpha \ge 2$ as well as for the deviations of Riesz’s means of order 2 of the Taylor series in the class of functions holomorphic in the disc and having a bounded derivative.
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