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On the diameters of certain classes of analytic functions. II

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Ukrainian Mathematical Journal Aims and scope

Abstract

In the spaces Eq(Ω), q≥1, we consider the classes WrEp(Ω), p≥1, consisting of analytic functions f(z) ε EP(Ω) the integral moduli of continuity of whose r-th derivatives are majorized by a given nonnegative nondecreasing function Φ.

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Literature cited

  1. S. B. Vakarchuk, “On the diameters of certain classes of analytic functions. I,” Ukr. Mat. Zh.,44, No. 3, 324–333 (1992).

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  2. V. N. Malozemov, Simultaneous Approximation of Functions and Their Derivatives [in Russian], Izdat. Leningr. Univ., Leningrad (1973).

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  3. M. I. Andrashko, “On approximations in the mean of analytic functions in regions with smooth boundaries,” Thesis Report, II All-Union Conference on the Constructive Theory of Functions (Baku, October 8–13, 1962), Izdat. Akad. Nauk Azerb. SSR, Baku (1962).

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Authors and Affiliations

  1. Institute of Geotechnical Mechanics, Ukrainian Academy of Sciences, Dnepropetrovsk

    S. B. Vakarchuk

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  1. S. B. Vakarchuk
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 8, pp. 1135–1138, August, 1992.

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Vakarchuk, S.B. On the diameters of certain classes of analytic functions. II. Ukr Math J 44, 1038–1040 (1992). https://doi.org/10.1007/BF01057128

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  • DOI: https://doi.org/10.1007/BF01057128

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