In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for functional classes of continuous functions. We use chaining technique to provide a general bound for the error of sampling discretization of the $L_p$-norm on a given functional class in terms of entropy numbers in the uniform norm of this class. The general result yields new error bounds for sampling discretization of the $L_p$-norms on classes of multivariate functions with mixed smoothness. In the second part of the paper we study universal sampling discretization and the problem of optimal sampling recovery.

翻译：本文第一部分研究了连续函数类上积分$L_p$范数的采样离散化绝对误差。我们利用链式技术，基于函数类在一致范数下的熵数，给出了该类$L_p$范数采样离散化误差的通用界。该通用结果导出了混合光滑性多元函数类上$L_p$范数采样离散化误差的新界。本文第二部分研究了通用采样离散化及最优采样恢复问题。