  In this paper, we study tractability of $L_2$-approximation of one-periodic
functions from weighted Korobov spaces in the worst-case setting. The
considered weights are of product form. For the algorithms we allow information
from the class $\Lambda^{{\rm all}}$ consisting of all continuous linear
functionals and from the class $\Lambda^{{\rm std}}$, which only consists of
function evaluations.
  We provide necessary and sufficient conditions on the weights of the function
space for quasi-polynomial tractability, uniform weak tractability, weak
tractability and $(\sigma,\tau)$-weak tractability. Together with the already
known results for strong polynomial and polynomial tractability, our findings
provide a complete picture of the weight conditions for all current standard
notions of tractability.
