标题： 精确不等式和基于不准确信息的最佳恢复 显示英文标题

标题： Exact inequalities and optimal recovery by inaccurate information

摘要： 本文考虑了一个多维最优恢复问题，即基于不准确指定的信息来恢复一个算子，该算子的作用表示为通过特殊类型的权函数乘以原始函数。 获得了一个此类算子范数的精确不等式。 所考虑的问题是对空间 $\mathbb R^d$ 中基于其他不准确指定导数的导数最优恢复问题以及精确不等式问题的推广，该精确不等式是 Hardy-Littlewood-Polya 不等式的类比。 显示英文摘要

摘要： The paper considers a multidimensional problem of optimal recovery of an operator whose action is represented by multiplying the original function by a weight function of a special type, based on inaccurately specified information about the values of operators of a similar type. An exact inequality for the norms of such operators is obtained. The problem under consideration is a generalization of the problem of optimal recovery of a derivative based on other inaccurately specified derivatives in the space $\mathbb R^d$ and the problem of an exact inequality, which is an analogue of the Hardy-Littlewood-Polya inequality.