Estimates for the approximation characteristics of the Nikol'skii-Besov classes of functions with mixed smoothness in the space B_q,1

2024/04/08 by Kateryna Pozharska, Pozharska, K. V., A. S. Romanyuk +1
Mathematics · #41A46 #41A50 #42A10 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.2404.05451

openalex publication_date 2024/04/08 · openalex created_date 2024/04/11 · openalex updated_date 2026/07/28

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 B^\boldsymbolr_{p, θ}) in the space B_q,1, 1 ≤ p, q ≤ ∞, which norm is stronger than the L_q-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 L_q. Besides, a significant progress is made in estimates for the considered approximation characteristics of the classes B^\boldsymbolr_{p, θ} in the space B_{q, 1} comparing to the known estimates in the space L_q.

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