Multivariate approximation by translates of the Korobov function on Smolyak grids

For a set W⊂Lp(Td)W⊂Lp(Td), 11/2, is especially important since K2r(Td) is a reproducing kernel Hilbert space, whose reproducing kernel is a translation kernel determined by κr,dκr,d. We also provide lower bounds of the optimal approximation on the best choice of φφ.