We study $L_2$-approximation problems in the worst case setting in the weighted Korobov spaces $H_{d,\a,{\bm \ga}}$ with parameters $1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$ and $\frac1 2<\az_1\le \az_2\le \cdots$. We consider the worst case error of algorithms that use finitely many arbitrary continuous linear functionals. We discuss the strongly polynomial tractability (SPT), polynomial tractability (PT), and $(t_1,t_2)$-weak tractability ($(t_1,t_2)$-WT) for all $t_1>1$ and $t_2>0$ under the absolute or normalized error criterion. In particular, we obtain the matching necessary and sufficient condition for SPT or PT in terms of the parameters.

翻译：我们在最差情形下研究加权Korobov空间$H_{d,\a,{\bm \ga}}$中的$L_2$逼近问题，其中参数满足$1\ge \ga_1\ge \ga_2\ge \cdots\ge 0$且$\frac1 2<\az_1\le \az_2\le \cdots$。我们考虑使用有限个任意连续线性泛函的算法的最差情形误差。在绝对或归一化误差准则下，我们讨论了强多项式可处理性（SPT）、多项式可处理性（PT）以及所有$t_1>1$和$t_2>0$时的$(t_1,t_2)$-弱可处理性（$(t_1,t_2)$-WT）。特别地，我们以参数形式得到了SPT或PT的匹配充分必要条件。