Exact-order estimates of multivariate periodic functions in Nikol'skii–Besov classes improve upon known results, suggesting significant advancements in approximation characteristics.
Exact‐order estimates are obtained for some approximation characteristics of the classes of periodic multivariate functions with mixed smoothness (the Nikol'skii–Besov classes ) in the space , , , whose norm is stronger than the ‐norm. It is shown that in the multivariate case (in contrast to the univariate) in most of the considered situations the obtained estimates differ in order from the corresponding estimates in the space . Besides, a significant progress is made in estimates for the considered approximation characteristics of the classes in the space comparing to the known estimates in the space .
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Pozharska et al. (2025) studied this question.
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