Estimates for approximation characteristics of Nikol'skii–Besov classes of functions with mixed smoothness in the space Bq,1${B_{q,1}}$

Abstract 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 .