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Average Widths and Optimal Recovery of Multivariate Besov Classes in Orlicz Spaces

Author

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  • Xinxin Li

    (College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
    Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Hohhot 010022, China
    Center for Applied Mathematical Science, Hohhot 010022, China)

  • Garidi Wu

    (College of Mathematics Science, Inner Mongolia Normal University, Hohhot 010022, China
    Laboratory of Infinite-Dimensional Hamiltonian System and Its Algorithm Application, Hohhot 010022, China
    Center for Applied Mathematical Science, Hohhot 010022, China)

Abstract

In this paper, we study the average Kolmogorov σ –widths and the average linear σ –widths of multivariate isotropic and anisotropic Besov classes in Orlicz spaces and give the weak asymptotic estimates of these two widths. At the same time, we also give the asymptotic property of the optimal recovery of isotropic Besov classes in Orlicz spaces.

Suggested Citation

  • Xinxin Li & Garidi Wu, 2024. "Average Widths and Optimal Recovery of Multivariate Besov Classes in Orlicz Spaces," Mathematics, MDPI, vol. 12(9), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1400-:d:1388243
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    References listed on IDEAS

    as
    1. Xinxin Li & Garidi Wu & Ding-Xuan Zhou, 2023. "Infinite Dimensional Widths and Optimal Recovery of a Function Class in Orlicz Spaces in L(R) Metric," Journal of Mathematics, Hindawi, vol. 2023, pages 1-13, September.
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