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Approximation of Holomorphic Functions by Cesàro Means

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Ukrainian Mathematical Journal Aims and scope

For the Lipschitz class of functions holomorphic in the disc, we present a constructive characteristic of this class in terms of the Cesàro means of order 𝛼 ≥ 2 for the Taylor series. We solve the problem of finding the exact upper bound for the deviations of the Cesàro means of order 𝛼 ≥ 2, as well as for the deviations of the Riesz means of order 2 for the Taylor series in the class of functions with bounded derivative holomorphic in the disc.

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

    O. G. Rovenska & V. V. Savchuk

  2. I. Sikorsky Kyiv Polytechnic Institute, National Technical University of Ukraine, Kyiv, Ukraine

    M. V. Savchuk

Authors
  1. O. G. Rovenska
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  2. V. V. Savchuk
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  3. M. V. Savchuk
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Correspondence to V. V. Savchuk.

Additional information

Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 676–684, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7143.

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Rovenska, O.G., Savchuk, V.V. & Savchuk, M.V. Approximation of Holomorphic Functions by Cesàro Means. Ukr Math J 74, 773–782 (2022). https://doi.org/10.1007/s11253-022-02100-7

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  • DOI: https://doi.org/10.1007/s11253-022-02100-7

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