On quasi-Monte Carlo methods in weighted ANOVA spaces

In the present paper we study quasi-Monte Carlo rules for approximating integrals over $d$-dimensional unit cube functions from weighted Sobolev spaces of regularity one. While properties these are well understood anchored spaces, this is not case ANOVA which another very important type reference rules. Using a direct approach provide formula worst error spaces. As consequence bound above in terms discrepancy employed integration nodes. On other hand also obtain general lower number $n$ used For one-dimensional our results lead to optimal rule and two-dimensional yielding convergence rates.