On tractability of weighted integration over bounded and unbounded regions in ℝ^{𝕤}

Hickernell, Fred; Sloan, Ian; Wasilkowski, Grzegorz

doi:10.1090/S0025-5718-04-01624-2

On tractability of weighted integration over bounded and unbounded regions in $\mathbb {R}^s$
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by Fred J. Hickernell, Ian H. Sloan and Grzegorz W. Wasilkowski PDF

Math. Comp. 73 (2004), 1885-1901 Request permission

Abstract:

We prove that for the space of functions with mixed first derivatives bounded in $L_1$ norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.

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