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 apply the obtained bounds to study universal sampling discretization and the problem of optimal sampling recovery.

翻译：本文第一部分研究连续函数函数类上积分$L_p$范数采样离散化的绝对误差。我们利用链式技巧，以该类函数在一致范数下的熵数为基础，给出了给定函数类上$L_p$范数采样离散化误差的一般性界。该一般性结果为具有混合光滑性的多元函数类上的$L_p$范数采样离散化提供了新的误差界。在第二部分中，我们将所获得的界应用于研究通用采样离散化及最优采样恢复问题。