Optimal Recovery on the Classes of Functions with Bounded Mixed Derivative

Temlyakov considered the optimal recovery on the classes of functions with bounded mixedderivative in the Lmetrics and gave the upper estimates of the optimal recovery errors. In this paper,we determine the asymptotic orders of the optimal recovery in Sobolev spaces by standard information,i.e., function values, and give the nearly optimal algorithms which attain the asymptotic orders of theoptimal recovery.