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Inequalities of the Markov–Nikol’skii Type in Regions with Zero Interior Angles in the Bergman Space

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Ukrainian Mathematical Journal Aims and scope

The order of growth of the module of an arbitrary algebraic polynomial in a weighted Bergman space Ap(G, h), p > 0, is studied in the regions with exterior nonzero and interior zero angles at finitely many points of the boundary. We establish Markov–Nikol’skii-type estimates for algebraic polynomials and clarify the behavior of derived polynomials at the points of zeros and poles of the weight function in bounded regions with piecewise-smooth boundary.

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Authors and Affiliations

  1. Gaziantep University, Gaziantep, Turkey

    Pelin Özkartepe

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  1. Pelin Özkartepe
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Correspondence to Pelin Özkartepe.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 75, No. 3, pp. 364–381, March, 2023. Ukrainian DOI: https://doi.org/10.37863/umzh.v75i3.7322.

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Özkartepe, P. Inequalities of the Markov–Nikol’skii Type in Regions with Zero Interior Angles in the Bergman Space. Ukr Math J 75, 419–438 (2023). https://doi.org/10.1007/s11253-023-02208-4

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  • DOI: https://doi.org/10.1007/s11253-023-02208-4

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