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Approximative characteristics of functions from the classes \( {S}_{p,\theta}^{\varOmega } \) B(ℝd) with a given majorant of mixed moduli of continuity

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Abstract

We obtain the exact-by-order estimates of the approximation of functions from the classes \( {S}_{p,\theta}^{\varOmega } \) B(ℝd) in the space Lq(ℝd), 1 < p < q < ∞, by entire functions of the exponential type with supports of their Fourier transforms in sets generated by the level surfaces of a function Ω.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Sergii Ya. Yanchenko & Sergii A. Stasyuk

Authors
  1. Sergii Ya. Yanchenko
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  2. Sergii A. Stasyuk
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Correspondence to Sergii Ya. Yanchenko.

Additional information

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 15, No. 1, pp. 132–148 January–March, 2018.

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Yanchenko, S.Y., Stasyuk, S.A. Approximative characteristics of functions from the classes \( {S}_{p,\theta}^{\varOmega } \) B(ℝd) with a given majorant of mixed moduli of continuity. J Math Sci 235, 103–115 (2018). https://doi.org/10.1007/s10958-018-4062-z

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  • DOI: https://doi.org/10.1007/s10958-018-4062-z

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