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

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 ).