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Bounds for the sampling discretization error and their applications to the universal sampling discretization
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abstract
In the first part of the paper we study absolute error of sampling discretization of the integral $L_p$-norm for function classes of continuous functions. We use basic approaches from chaining technique to provide general upper bounds for the error of sampling discretization of the $L_p$-norm on a given function class in terms of entropy numbers in the uniform norm of this class. As an example we apply these general results to obtain 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 our general bounds to study the problem of universal sampling discretization.
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Cited by 1 Pith paper
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Some lower bounds for optimal sampling recovery of functions with mixed smoothness
Optimal nonlinear sampling recovery of mixed-smoothness classes H^r_q is at least c m^{-r+1/q-1/p} (log m)^{(d-1)/p}, a logarithmic factor not captured by previous lower-bound techniques.
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