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Characteristics of the linear and nonlinear approximations of the Nikol’skii–Besov-type classes of periodic functions of several variables

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Abstract

Estimates that are accurate by order of magnitude have been obtained for some characteristics of the linear and nonlinear approximations of the isotropic classes of the Nikol’skii–Besov-type \({\mathbf{B}}_{p,\theta }^{\omega }\) of periodic functions of several variables in the spaces Bq,1, 1 ≤ q ≤ ∞. A specific feature of those spaces, as linear subspaces of Lq, is that the norm in them is “stronger” than the Lq-norm.

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Authors and Affiliations

  1. Lesya Ukrainka Volyn National University, Lutsk, Ukraine

    Svitlana B. Hembars’ka, Ihor A. Romanyuk & Oksana V. Fedunyk-Yaremchuk

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  1. Svitlana B. Hembars’ka
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  2. Ihor A. Romanyuk
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  3. Oksana V. Fedunyk-Yaremchuk
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Correspondence to Svitlana B. Hembars’ka.

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Presented by R. M. Trygub

Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 20, No. 2, pp. 161–185, April–June, 2

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Hembars’ka, S.B., Romanyuk, I.A. & Fedunyk-Yaremchuk, O.V. Characteristics of the linear and nonlinear approximations of the Nikol’skii–Besov-type classes of periodic functions of several variables. J Math Sci 274, 307–326 (2023). https://doi.org/10.1007/s10958-023-06602-y

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