We establish order estimates for the entropy numbers of the classes \( {B}_{p,\theta}^{\varOmega } \) of periodic multivariable functions in the uniform metric. For the proper choice of the functions Ω, these classes coincide with the Nikol’skii–Besov classes \( {B}_{p,\theta}^r. \)
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, No. 9, pp. 1249–1263, September, 2018.
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Pozhars’ka, K.V. Estimates for the Entropy Numbers of the Classes \( {B}_{p,\theta}^{\varOmega } \) of Periodic Multivariable Functions in the Uniform Metric. Ukr Math J 70, 1439–1455 (2019). https://doi.org/10.1007/s11253-019-01578-y
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DOI: https://doi.org/10.1007/s11253-019-01578-y