It is known that results on universal sampling discretization of the square norm are useful in sparse sampling recovery with error measured in the square norm. In this paper we demonstrate how known results on universal sampling discretization of the uniform norm and recent results on universal sampling representation allow us to provide good universal methods of sampling recovery for anisotropic Sobolev and Nikol'skii classes of periodic functions of several variables. The sharpest results are obtained in the case of functions on two variables, where the Fibonacci point sets are used for recovery.

翻译：众所周知，平方范数的通用采样离散化结果对于以平方范数衡量误差的稀疏采样恢复具有重要意义。本文展示了均匀范数的通用采样离散化已知结果以及近期关于通用采样表示的研究成果，如何使我们能够为各向异性的Sobolev类和Nikol'skii类多元周期函数提供有效的通用采样恢复方法。在二元函数情形下获得了最精确的结果，此时采用Fibonacci点集进行恢复。