Quasi-Monte Carlo Integration in the Mixed Korobov–Sobolev Type Space $$H_{Mix, s, \alpha, \gamma, w}$$

Abstract

In this article, the authors construct a special reproducing kernel Hilbert space of mixed Korobov–Sobolev type. To address the main problems, an appropriate hybrid function system is employed. The arithmetic associated with this function system is used to define the notion of the mean square worst-case error of the integration in the considered space. An explicit formula for this error expressed in terms of the functions of the employed system is obtained.