论文标题
从某种域中属于尼古尔斯基 - 贝索夫的属性属性的函数值重建衍生物
Reconstructing derivatives from values of functions belonging to Nikolskii-Besov classes of mixed smoothness in domains of a certain kind
论文作者
论文摘要
本文研究了使用“ $ l_p $ -Averaged”连续性的混合模量定义的Nikolskii和BESOV空间，用于适当订单的函数，而不是某些混合衍生功能的已知阶连续性混合模量。这项工作提供了从某种类型的有限域中的此类函数类别的函数值以给定数量的函数值的重建衍生物的最佳准确性的上下估计值。这些估计数并不弱，但在某些情况下，这些估计比作者在考虑到Cube $ i^d的上述功能类别的问题中所提出的问题甚至更强。 $它还显着拓宽了尼古斯基（Nikolskii）的类别和混合光滑度的BESOV空间，其中提出了所考虑的问题中提到的估计值。
The article examines Nikolskii and Besov spaces with norms defined using "$L_p$-averaged" mixed moduli of continuity for functions of appropriate orders, instead of mixed moduli of continuity of known orders for certain mixed derivative functions. The work provides upper and lower estimates of the best accuracy of reconstruction derivatives from function values at a given number of points for such classes of functions in bounded domains of a certain kind. These estimates are not weaker, but in some cases even stronger than those derived by the author in the problem under consideration for the aforementioned classes of functions on cube $ I^d. $ It also significantly broadens the class of Nikolskii and Besov spaces of mixed smoothness for which mentioned estimates in the problem under consideration have been derived.
