2019
Том 71
№ 9

# Constructive Characteristic of ho¨ Lder Classes and M-Term Approximations in the Multiple Haar Basis

Romanyuk V. S.

Abstract

In terms of the best polynomial approximations in the multiple Haar basis, we obtain a constructive characteristic of the Hölder classes H p α of functions defined on the unit cube $\mathbb{I}$ d of the space ℝ d 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 p α in the Lebesgue spaces L q ( $\mathbb{I}$ d ).

English version (Springer): Ukrainian Mathematical Journal 66 (2014), no. 3, pp 391-403.

Citation Example: Romanyuk V. S. Constructive Characteristic of ho¨ Lder Classes and M-Term Approximations in the Multiple Haar Basis // Ukr. Mat. Zh. - 2014. - 66, № 3. - pp. 349–360.

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