Tractability of approximation in the weighted Korobov space in the worst-case setting — a complete picture

In this paper, we study tractability of L2-approximation one-periodic functions from weighted Korobov spaces in the worst-case setting. The considered weights are product form. For algorithms allow information class ?all consisting all continuous linear functionals and ?std, which only consists function evaluations. We provide necessary sufficient conditions on space for quasi-polynomial tractability, uniform weak (?,?)-weak tractability. Together with already known results strong polynomial our findings a complete picture weight current standard notions