Estimates for the approximation characteristics of the Nikol'skii-Besov classes of functions with mixed smoothness in the space $B_{q,1}$
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866929561612058624 |
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| author | Pozharska, K. V. Romanyuk, A. S. |
| author_facet | Pozharska, K. V. Romanyuk, A. S. |
| contents | Exact-order estimates are obtained for some approximation characteristics of the classes of periodic multivariate functions with mixed smoothness (the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p, θ}$) in the space $B_{q,1}$, $1 \leq p, q \leq \infty$, 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 $B^{\boldsymbol{r}}_{p, θ}$ in the space $B_{q, 1}$ comparing to the known estimates in the space $L_q$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05451 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Estimates for the approximation characteristics of the Nikol'skii-Besov classes of functions with mixed smoothness in the space $B_{q,1}$ Pozharska, K. V. Romanyuk, A. S. Classical Analysis and ODEs 41A46, 41A50, 42A10 Exact-order estimates are obtained for some approximation characteristics of the classes of periodic multivariate functions with mixed smoothness (the Nikol'skii-Besov classes $B^{\boldsymbol{r}}_{p, θ}$) in the space $B_{q,1}$, $1 \leq p, q \leq \infty$, 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 $B^{\boldsymbol{r}}_{p, θ}$ in the space $B_{q, 1}$ comparing to the known estimates in the space $L_q$. |
| title | Estimates for the approximation characteristics of the Nikol'skii-Besov classes of functions with mixed smoothness in the space $B_{q,1}$ |
| topic | Classical Analysis and ODEs 41A46, 41A50, 42A10 |
| url | https://arxiv.org/abs/2404.05451 |