For kernels with mixed smoothness r>1, the worst-case entropy numbers of the associated L1-to-L∞ integral operator classes decay like k^{-2r} up to logarithmic factors in dimensions one and two.
Temlyakov, Estimates of the best bilinear approximations of functions of two variables and some of their applications, Mat
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Entropy numbers of classes defined by integral operators
For kernels with mixed smoothness r>1, the worst-case entropy numbers of the associated L1-to-L∞ integral operator classes decay like k^{-2r} up to logarithmic factors in dimensions one and two.