In terms of the best polynomial approximations in the multiple Haar basis, we obtain a constructive characteristic of the Hölder classes H α p of functions defined on the unit cube \( \mathbb{I} \) d of the space ℝd under the restriction \( 0<\alpha <\frac{1}{p}\le 1 \). We also solve the problem of order estimates of the best m-term approximations in the Haar basis of classes H α p in the Lebesgue spaces L q (\( \mathbb{I} \) d).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 66, No. 3, pp. 349–360, March, 2014.
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Romanyuk, V.S. Constructive Characteristic of ho¨ Lder Classes and M-Term Approximations in the Multiple Haar Basis. Ukr Math J 66, 391–403 (2014). https://doi.org/10.1007/s11253-014-0938-3
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DOI: https://doi.org/10.1007/s11253-014-0938-3