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.
Temlyakov, On a way of obtaining lower estimates for the er- rors of quadrature formulas, Matem
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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.