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

Sergii Ya. Yanchenko; Sergii A. Stasyuk

doi:10.1007/s10958-018-4062-z

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

Authors: Yanchenko S.Y.¹, Stasyuk S.A.¹
Affiliations:
1. Institute of Mathematics of the NAS of Ukraine
Issue: Vol 235, No 1 (2018)
Pages: 103-115
Section: Article
URL: https://journals.rcsi.science/1072-3374/article/view/242066
DOI: https://doi.org/10.1007/s10958-018-4062-z
ID: 242066

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Abstract
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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(ℝ^d) in the space L_q(ℝ^d), 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.

Keywords

Nikol’skii–Besov spaces, mixed modulus of continuity, best approximation, entire function of the exponential type, Fourier transform

About the authors

Sergii Ya. Yanchenko

Institute of Mathematics of the NAS of Ukraine

Author for correspondence.
Email: Yan.Sergiy@gmail.com
Ukraine, Kiev

Sergii A. Stasyuk