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

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematische Nachrichten Pub Date : 2025-08-05 DOI:10.1002/mana.70027

K. V. Pozharska, A. S. Romanyuk

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引用次数: 0

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 $B_{p, θ}^{r}$ ) in the space $B_{q, 1}$ , $1 \leq p, q \leq \infty$ , $1 \leq θ \leq \infty$ , whose 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 $B_{p, θ}^{r}$ in the space $B_{q, 1}$ comparing to the known estimates in the space $L_{q}$ .

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空间bq，1 ${B_{q,1}}$中混合光滑函数Nikol 'skii-Besov类的逼近特征估计

得到了混合光滑周期多元函数类（Nikol 'skii-Besov类B p， B p, B p）的一些近似特征的正序估计。θ r $B^{\bm{r}}_{p, \theta }$)在空间B q， 1 $B_{q,1}$, 1≤p，q≤∞$1 \le p, q \le \infty$, 1≤θ≤∞$1\le \theta \le \infty$，其范数强于L q $L_q$ -范数。结果表明，在多元情况下（与单变量情况相反），在大多数考虑的情况下，得到的估计与空间lq $L_q$中相应的估计顺序不同。此外，在对B q空间中B p， θ r $B^{\bm{r}}_{p, \theta }$类所考虑的近似特性的估计方面取得了重大进展。1 $B_{q, 1}$与空间lq $L_q$中已知的估计值进行比较。

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来源期刊

Mathematische Nachrichten 数学-数学

CiteScore

1.50

自引率

0.00%

发文量

157

审稿时长

4-8 weeks

期刊介绍： Mathematische Nachrichten - Mathematical News publishes original papers on new results and methods that hold prospect for substantial progress in mathematics and its applications. All branches of analysis, algebra, number theory, geometry and topology, flow mechanics and theoretical aspects of stochastics are given special emphasis. Mathematische Nachrichten is indexed/abstracted in Current Contents/Physical, Chemical and Earth Sciences; Mathematical Review; Zentralblatt für Mathematik; Math Database on STN International, INSPEC; Science Citation Index