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

Bounds for the sampling discretization error and their applications to universal sampling discretization