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One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables

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Ukrainian Mathematical Journal Aims and scope

We obtain a new sharp inequality of the Landau–Kolmogorov type for a periodic function of two variables estimating the convolution of the best uniform approximations of its partial primitives by the sums of functions of single variable via the L∞-norm of the function itself and uniform norms of its mixed primitives. Some applications of the obtained inequality are also presented.

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Authors and Affiliations

  1. Dnepr National University, Dnepr, Ukraine

    V. F. Babenko

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  1. V. F. Babenko
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Correspondence to V. F. Babenko.

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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 2, pp. 158–167, February, 2019.

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Babenko, V.F. One Inequality of the Landau–Kolmogorov Type for Periodic Functions of Two Variables. Ukr Math J 71, 179–189 (2019). https://doi.org/10.1007/s11253-019-01637-4

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  • DOI: https://doi.org/10.1007/s11253-019-01637-4

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