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Direct and Inverse Approximation Theorems in the Besicovitch–Musielak–Orlicz Spaces of Almost Periodic Functions

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Ukrainian Mathematical Journal Aims and scope

In terms of the best approximations of functions and generalized moduli of smoothness, direct and inverse approximation theorems are proved for the Besicovitch almost periodic functions whose Fourier exponent sequences have a single limit point at infinity and their Orlicz norms are finite. Special attention is given to the study of cases where the constants in these theorems are unimprovable.

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Authors and Affiliations

  1. Donbas State Pedagogical University, Sloviansk, Donetsk Oblast, Ukraine

    S. O. Chaichenko & T. V. Shulyk

  2. Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine and National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine

    A. L. Shidlich

Authors
  1. S. O. Chaichenko
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  2. A. L. Shidlich
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  3. T. V. Shulyk
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Correspondence to A. L. Shidlich.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 74, No. 5, pp. 701–716, May, 2022. Ukrainian DOI: https://doi.org/10.37863/umzh.v74i5.7045.

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Chaichenko, S.O., Shidlich, A.L. & Shulyk, T.V. Direct and Inverse Approximation Theorems in the Besicovitch–Musielak–Orlicz Spaces of Almost Periodic Functions. Ukr Math J 74, 801–819 (2022). https://doi.org/10.1007/s11253-022-02102-5

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  • DOI: https://doi.org/10.1007/s11253-022-02102-5

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